Transmission device and transmission method

ABSTRACT

A first transmission signal and a second transmission signal are generated from a first modulated signal and a second modulated signal by using a precoding matrix, and parameters of the precoding matrix are calculated from feedback information.

TECHNICAL FIELD

The present disclosure relates to transmission techniques using multipleantennas.

BACKGROUND ART

One conventional communications method that uses multiple antennas is,for example, the communications method known as Multiple-InputMultiple-Out (MIMO).

In multi-antenna communications, which is typically MIMO, data receptionquality and/or a data communication rate (per unit time) can be improvedby modulating transmission data of one or more sequences andsimultaneously transmitting the respective modulated signals fromdifferent antennas by using the same frequency (common frequency).

One type of MIMO is polarized MIMO. For example, Patent Literature (PTL)1 (Japanese Unexamined Patent Application Publication No. 2007-192658)discloses the following.

The rank of the channel matrix is improved and the stream count ensuredby switching polarization surfaces of some antennas on the transmittingside and receiving side, and approximating a transfer function betweenan antenna using a polarization surface that is orthogonal to thesepolarization surfaces to 0. When the antenna configuration is 3×3 orlarger, typically all antennas use vertical polarization, and it isdetermined to which antennas horizontal polarization should be appliedto effectively improve channel matrix quality, and the polarizationsurfaces are switched for only specified antennas in the transceiver.

CITATION LIST Patent Literature

PTL 1: Japanese Unexamined Patent Application Publication No.2007-192658

SUMMARY OF THE INVENTION

In MIMO, processing may be performed in which weighting calculation isperformed on mapped signal s₁(t) and mapped signal s₂(t) using aprecoding matrix to generate weighted signal r₁(t) and weighted signalr₂(t).

However, PTL 1 does not disclose changing the precolling matrix whiletaking polarization into account.

In view of this, one aspect of the present disclosure is to provide atransmission device and transmission method that change the precollingmatrix, taking into account polarization.

A transmission method according to one aspect of the present disclosureis a method including: generating and transmitting a first transmissionsignal z₁(t) and a second transmission signal z₂(t) by calculating MATH.4 (to be described later) from a first modulated signal s₁(t) and asecond modulated signal s₂(t); and calculating θ, a, and b based onfeedback information so as to satisfy MATH. 7.

General or specific aspects of these may be realized as a system,method, integrated circuit, computer program, storage medium, or anygiven combination thereof.

With this, it is possible to improve reception performance on thereceiving side since the precoding matrix is changed taking into accountpolarization.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a system configuration diagram of a polarized MIMO system.

FIG. 2 illustrates one example of an arrangement state of antennas.

FIG. 3 illustrates one example of a configuration of a communicationsstation.

FIG. 4 illustrates another example of a configuration of acommunications station.

FIG. 5 illustrates one example of a frame configuration of a modulatedsignal of a communications station.

FIG. 6 illustrates one example of a configuration of a terminal.

FIG. 7 illustrates one example of a frame configuration of a modulatedsignal of a terminal.

FIG. 8 illustrates one example of a communication state between acommunications station and a terminal.

FIG. 9 illustrates another example of a frame configuration of amodulated signal of a communications station.

FIG. 10 illustrates an example of a configuration of a communicationsstation.

FIG. 11 illustrates an example of a configuration of a communicationsstation.

FIG. 12 illustrates an example of a configuration of a communicationsstation.

FIG. 13 illustrates an example of a configuration of a communicationsstation.

FIG. 14 illustrates an example of a phase changing method.

FIG. 15 illustrates an example of a phase changing method.

FIG. 16 illustrates an example of a frame configuration.

FIG. 17 illustrates an example of a frame configuration.

FIG. 18 illustrates an example of a frame configuration.

FIG. 19 illustrates an example of a frame configuration.

FIG. 20 illustrates an example of a frame configuration.

FIG. 21 illustrates an example of a frame configuration.

FIG. 22 illustrates an example of a frame configuration.

FIG. 23 illustrates an example of a phase changing method.

FIG. 24 illustrates an example of a phase changing method.

FIG. 25 illustrates an example of a mapper.

FIG. 26 illustrates an example of a configuration of a communicationsstation.

FIG. 27 illustrates an example of a configuration of a communicationsstation.

DESCRIPTION OF EXEMPLARY EMBODIMENTS Embodiments

Hereinafter, embodiments according to the present disclosure will bedescribed with reference to the drawings.

(MIMO Polarization)

FIG. 1 is a system configuration diagram of a polarized MIMO system.

Transmitter 111 of communications station 110 receives an input ofsignal z₁(t) and signal z₂(t). Transmitter 111 transmits signal z₁(t)from horizontal vertical polarizing antenna 112 and transmits signalz₂(t) from vertical polarizing antenna 113.

Receiver 151 of terminal 150 receives an input of a signal received byhorizontal polarizing antenna 152 and a signal received by verticalpolarizing antenna 154, and outputs signal r₁(t) and signal r₂(t).

Here, the channel characteristics between horizontal polarizing antenna112 of communications station 110 and horizontal polarizing antenna 152of terminal 150 is h₁₁(t), the channel characteristics between verticalpolarizing antenna 113 of communications station 110 and horizontalpolarizing antenna 152 of terminal 150 is h₁₂(t), the channelcharacteristics between horizontal polarizing antenna 112 ofcommunications station 110 and vertical polarizing antenna 152 ofterminal 150 is h₂₁(t), and the channel characteristics between verticalpolarizing antenna 113 of communications station 110 and verticalpolarizing antenna 153 of terminal 150 is h₂₂(t).

In this case

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 1} \right\rbrack & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} & (1)\end{matrix}$

holds true.

Then, in a polarized Multiple-Input Multiple Output (MIMO) system, whenthe cross polarization discrimination (XPD) is a large value, h₁₂(t) andh₂₁(t) can be treated as h₁₂(t)≈0 and h₂₁(t)≈0. Then, when themillimeter waveband is used, since the radio waves have strong straighttravelling properties, there is a high probability of the followingcircumstance.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 2} \right\rbrack & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} & (2)\end{matrix}$

Here, if z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), mapped baseband signal s₁(t) is not affected(interference) by mapped baseband signal s₂(t), and thus achievingfavorable data reception quality is likely. Similarly, since mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t), achieving favorable data reception quality is likely.

However, h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t) are complex numbers (may beactual numbers). r₁(t), r₂(t), z₁(t), and z₂(t) are complex numbers (maybe actual numbers). n₁(t) and n₂(t) are noise, and are complex numbers.

FIG. 2 illustrates one example of an arrangement state of antennas.

In FIG. 2, an ideal state of an arrangement of horizontal polarizingantenna 152 and vertical polarizing antenna 153 on the receiving siderelative to horizontal polarizing antenna 112 and vertical polarizingantenna 113 on the transmitting side is shown by dotted lines.

As illustrated in FIG. 2, the angle between horizontal polarizingantenna 152 and vertical polarizing antenna 153 in the ideal state andhorizontal polarizing antenna 152 and vertical polarizing antenna 153when in a state in which they are actually installed or when the antennastate is changed, is 6 (radians).

(Precoding Method (1A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 3} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (3)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 4} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (4)\end{matrix}$

(a, b are complex numbers (may be actual numbers))

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 5} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (5)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 6]

h ₁₁(t)×a×cos δ×sin θ+h ₂₂(t)×b×sin δ×cos θ=0   (6-1)

h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (6-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 7} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {7\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {7\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 8} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {8\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {8\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 9]

|a| ² +|b| ² =|u| ²   (9)

(|u|² is a parameter based on average transmitted power)

(Communications Station Configuration (1))

Hereinafter, one example of a configuration of a communications stationaccording to the present disclosure will be described. FIG. 3 is a blockdiagram illustrating one example of a configuration of a communicationsstation according to the present disclosure.

Communications station 300 includes: interleavers 302A, 302B; mappers304A, 304B; weighting synthesizers 306A, 306B; radio units 308A, 308B;horizontal polarizing antenna 310A; vertical polarizing antenna 310B;antenna 312; reception device 313; precoding method determiner 316; andtransmission method/frame configuration determiner 318.

Interleaver 302A receives inputs of encoded data 301A and transmissionmethod/frame configuration signal 319, interleaves encoded data 301A,and outputs interleaved data 303A. Note that the interleaving method maybe switched based on transmission method/frame configuration signal 319.

Interleaver 302B receives inputs of encoded data 301B and transmissionmethod/frame configuration signal 319, interleaves encoded data 301B,and outputs interleaved data 303B. Note that the interleaving method maybe switched based on transmission method/frame configuration signal 319.

Mapper 304A receives inputs of interleaved data 303A and transmissionmethod/frame configuration signal 319, applies a modulation such asQuadrature Phase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation(16QAM), or 64 Quadrature Amplitude Modulation (64QAM) to interleaveddata 303A, and outputs modulated signal (mapped signal) 305A. Note thatthe modulation method may be switched based on transmission method/frameconfiguration signal 319.

Mapper 304B receives inputs of interleaved data 303B and transmissionmethod/frame configuration signal 319, applies a modulation such asQuadrature Phase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation(16 QAM), or 64 Quadrature Amplitude Modulation (64QAM) to interleaveddata 303B, and outputs modulated signal (mapped signal) 305B. Note thatthe modulation method may be switched based on transmission method/frameconfiguration signal 319.

Weighting synthesizer 306A receives inputs of mapped signal 305A, mappedsignal 305B, transmission method/frame configuration signal 319, andprecoding method signal 320, weighting synthesizes mapped signal 305Aand mapped signal 305B based on precoding method signal 320, and outputsweighted signal 307A based on the frame configuration of transmissionmethod/frame configuration signal 319. Note that the weighting synthesismethod used by weighting synthesizer 306A will be described later.

Weighting synthesizer 306B receives inputs of mapped signal 305A, mappedsignal 305B, transmission method/frame configuration signal 319, andprecoding method signal 320, weighting synthesizes mapped signal 305Aand mapped signal 305B based on precoding method signal 320, and outputsweighted signal 307B based on the frame configuration of transmissionmethod/frame configuration signal 319. Note that the weighting synthesismethod used by weighting synthesizer 306B will be described later.

Radio unit 308A receives inputs of weighted signal 307A and transmissionmethod/frame configuration signal 319, applies processing such asorthogonal modulation, bandlimiting, frequency conversion, and/oramplification to weighted signal 307A, and outputs transmission signal309A. Transmission signal 309A is output from horizontal polarizingantenna 310A as radio waves. Note that the processing to be applied maybe switched based on transmission method/frame configuration signal 319.

Radio unit 308B receives inputs of weighted signal 307B and transmissionmethod/frame configuration signal 319, applies processing such asorthogonal modulation, bandlimiting, frequency conversion, and/oramplification to weighted signal 307B, and outputs transmission signal309B. Transmission signal 309B is output from vertical polarizingantenna 310B as radio waves. Note that the processing to be applied maybe switched based on transmission method/frame configuration signal 319.

Reception device 313 receives an input of reception signal 312 receivedby antenna 311, demodulates/decodes reception signal 312, and outputsthe resulting data signals 314, 315.

Precoding method determiner 316 receives inputs of data signal 314 andsignal 317, obtains, from data signal 314, feedback informationtransmitted by a communication partner, determines a precoding methodbased on feedback information, and outputs precoding method signal 320.Note that the determination of a precoding method by precoding methoddeterminer 316 will be described later.

Transmission method/frame configuration determiner 318 receives inputsof data signal 314 and signal 317, and obtains, from data signal 314,feedback information transmitted by a communication partner. Signal 317includes information on the transmission method requested by thecommunications station. Transmission method/frame configurationdeterminer 318 determines a transmission method/frame configurationbased on this information, and outputs transmission method/frameconfiguration signal 319.

(Communications Station Configuration (2))

Hereinafter, another example of a configuration of the communicationsstation according to the present disclosure will be described.

FIG. 4 is a block diagram illustrating another example of aconfiguration of a communications station according to the presentdisclosure.

In contrast to communications station 300 illustrated in FIG. 3,communications station 400 illustrated in FIG. 4 includes coefficientmultiplier 401A between weighting synthesizer 306A and radio unit 308A,and coefficient multiplier 401B between weighting synthesizer 306B andradio unit 308B.

Coefficient multiplier 401A receives inputs of weighted signal 307A andprecoding method signal 320, multiplies a coefficient with weightedsignal 307A based on precoding method signal 320, and outputscoefficient multiplied signal 402A. Note that the coefficientmultiplication by coefficient multiplier 401A will be described later.

Coefficient multiplier 401B receives inputs of weighted signal 307B andprecoding method signal 320, multiplies a coefficient with weightedsignal 307B based on precoding method signal 320, and outputscoefficient multiplied signal 402B. Note that the coefficientmultiplication by coefficient multiplier 401B will be described later.

Note that radio unit 308A illustrated in FIG. 4 performs processing oncoefficient multiplied signal 402A as an input instead of weightedsignal 307A, and radio unit 308B performs processing on coefficientmultiplied signal 402B as an input instead of weighted signal 307B.

(Precoding Method (1A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 10} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (10)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 11]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (11)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 12]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (12)

Precoding method determiner 316 performs the calculations described in“(precoding method (1A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 13} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {a \times \sin \; \theta} \\{b \times \sin \; \theta} & {{- b} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (13)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 14} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {14\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {14\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (1A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 15} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (15)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 16]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (16)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 17]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (17)

Precoding method determiner 316 performs the calculations described in“(precoding method (1A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 18} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}} & (18)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 19} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {19\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {19\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (1B))

As described in “(precoding method (1A))”, the following relationequation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 20} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (20)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 21]

h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (21-1)

h ₁₁(t)×a×sin δ×sin θ−h ₂₂(t)×b×cos δ×cos θ=0   (21-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 22} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {22\text{-}1} \right) \\{\theta = {{- \theta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {22\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 23} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {23\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {23\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 24]

|a| ² +|b| ² =|u| ²   (24)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (1B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 25} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (25)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 26]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (26)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 27]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (27)

Precoding method determiner 316 performs the calculations described in“(precoding method (1B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 28} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {a \times \sin \; \theta} \\{b \times \sin \; \theta} & {{- b} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (28)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 29} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {29\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {29\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (1B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 30} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (30)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 31]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (31)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 32]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (32)

Precoding method determiner 316 performs the calculations described in“(precoding method (1B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 33} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}} & (33)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 34} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {34\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {34\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Transmission Frame Configuration of Communications Station (1))

FIG. 5 illustrates one example of a frame configuration of a modulatedsignal transmitted by a communications station. In FIG. 5, time isrepresented on the horizontal axis and frequency is represented on thevertical axis. Note that in the frequency on vertical axis, one or morecarriers (subcarriers) is sufficient. In FIG. 5, (A) illustrates oneexample of a frame configuration of modulated signal (z₁(t)) transmittedfrom horizontal polarizing antenna 310A illustrated in FIG. 3, FIG. 4,and (B) illustrates one example of a frame configuration of modulatedsignal (z₂(t)) transmitted from vertical polarizing antenna 310Billustrated in FIG. 3, FIG. 4.

Moreover, the preamble, control information symbol, and precodingsettings training symbol may be single-carrier (one carrier), the datasymbol may be multi-carrier, such as orthogonal frequency-divisionmultiplexing (OFDM). (Here, the frequency band used to transmit apreamble, the frequency band used to transmit a control informationsymbol, the frequency band used to transmit a precoding settingstraining symbol, and the frequency band used to transmit a data symbolmay be the same or may be different.) Moreover, the preamble, controlinformation symbol, precoding settings training symbol, and data symbolmay be multi-carrier such as OFDM (here, the frequency band used totransmit a preamble, the frequency band used to transmit a controlinformation symbol, the frequency band used to transmit a precodingsettings training symbol, and the frequency band used to transmit a datasymbol may be the same or may be different).

Each preamble illustrated in FIG. 5 is a symbol including, for example,a signal for a terminal to detect a modulated signal transmitted by acommunications station, and a signal for the terminal to performtime-synchronization or frequency-synchronization with respect to amodulated signal transmitted by a communications station. Note that inFIG. 5, the preambles may be transmitted from both horizontal polarizingantenna 310A and vertical polarizing antenna 310B, and may betransmitted from one or the other of horizontal polarizing antenna 310Aand vertical polarizing antenna 310B.

Each control information symbol illustrated in FIG. 5 is a symbol fortransmitting control information to a terminal. The control informationsymbol includes, for example, information on the modulation method (of adata symbol) (information on the modulation method of s₁(t), andinfromation on the modulation method of s₂(t) (data symbol)),information on an error correction code used by a communications station(encode rate, block length (code length), etc.). A terminal obtains thecontrol information symbol and obtains information on the modulationmethod and information on the error correction code, thereby makingdemodulation/decoding of the data symbol possible. Note that in FIG. 5,the control information symbols may be transmitted from both horizontalpolarizing antenna 310A and vertical polarizing antenna 310B, and may betransmitted from one or the other of horizontal polarizing antenna 310Aand vertical polarizing antenna 310B.

Note that at least the data symbol is presumed to be MIMO transmitted,and the data symbols are transmitted from horizontal polarizing antenna310A and vertical polarizing antenna 310B at the same time and at thesame frequency.

Each reference symbol illustrated in FIG. 5 is a symbol for performingestimation (channel estimation) of a propagation environment, in orderfor a terminal to demodulate (perform wave detection on) a data symbol.The reference symbol is transmitted from horizontal polarizing antenna310A. The reference symbol may also be transmitted from verticalpolarizing antenna 310B. Note that “a reference symbol is not to betransmitted from vertical polarizing antenna 310B during the time and atthe frequency that a reference symbol is transmitted from horizontalpolarizing antenna 310A” may be a rule, and “a reference symbol is to betransmitted from vertical polarizing antenna 310B during the time and atthe frequency that a reference symbol is transmitted from horizontalpolarizing antenna 310A” may be a rule.

Each data symbol illustrated in FIG. 5 is a symbol for transmittingdata. The data symbol illustrated in (A) in FIG. 5 is signal z₁(t)configured from s₁(t) and/or s₂(t). The data symbol illustrated in (B)in FIG. 5 is signal z₂(t) configured from s₁(t) and/or s₂(t). Moreover,the data symbol illustrated in (A) in FIG. 5 and the data symbolillustrated in (B) in FIG. 5 are transmitted from the communicationsstation at the same time and using the same frequency.

Each precoding settings training symbol illustrated in FIG. 5 is atraining symbol for estimating parameters (a, b, θ) for performing theprecoding described in “(precoding method (1A))”, “(precoding method(1A-1))”, “(precoding method (1A-2))”, “(precoding method (1B))”,“(precoding method (1B-1))”, “(precoding method (1B-2))”. For example, aterminal receives a precoding settings training symbol, performsestimation (channel estimation) of a propagation environment, andtransmits a channel estimation value (channel state information (CSI))to the communications station. The precoding settings training symbol istransmitted from horizontal polarizing antenna 310A. The precodingsettings training symbol may also be transmitted from verticalpolarizing antenna 310B. Note that “a precoding settings training symbolis not to be transmitted from vertical polarizing antenna 310B duringthe time and at the frequency that a precoding settings training symbolis transmitted from horizontal polarizing antenna 310A” may be a rule,and “a precoding settings training symbol is to be transmitted fromvertical polarizing antenna 310B during the time and at the frequencythat a precoding settings training symbol is transmitted from horizontalpolarizing antenna 310A” may be a rule.

Note that the frame configuration illustrated in FIG. 5 of a modulatedsignal transmitted by the communications station is merely one example;symbols other than those illustrated in FIG. 5 may be transmitted by thecommunications station, and symbols other than those illustrated in FIG.5 may be present in the frame. Moreover, a pilot symbol for performingestimation (channel estimation) of a propagation environment may beinserted in, for example, the control information symbol or data symbol.

(Terminal Configuration)

FIG. 6 is a block diagram illustrating one example of a configuration ofa terminal according to the present disclosure.

Terminal 600 includes horizontal polarizing antenna 601_X, radio unit603_X, modulated signal z1 channel fluctuation estimator 605_1,modulated signal z2 channel fluctuation estimator 605_2, radio unit603_Y, modulated signal z1 channel fluctuation estimator 607_1,modulated signal z2 channel fluctuation estimator 607_2, controlinformation decoder 609, signal processor 611, feedback informationgenerator 613, time/frequency synchronizer 615, transmitter 618, andantenna 620.

Radio unit 603_X receives inputs of reception signal 602_X received byhorizontal polarizing antenna 601_X and time/frequency synchronizationsignal 616, applies processing such as frequency conversion and/ororthogonal demodulation to reception signal 602_X, and outputs basebandsignal 604_X.

Modulated signal z1 channel fluctuation estimator 605_1 receives inputsof baseband signal 604_X and time/frequency synchronization signal 616,performs channel estimation (calculates channel characteristics h₁₁(t))by using the reference symbol illustrated in (A) in FIG. 5, and outputschannel estimation signal 606_1.

Modulated signal z2 channel fluctuation estimator 605_2 receives inputsof baseband signal 604_X and time/frequency synchronization signal 616,performs channel estimation (calculates channel characteristics h₁₂(t))by using the reference symbol illustrated in (B) in FIG. 5, and outputschannel estimation signal 606_2.

Radio unit 603_Y receives inputs of reception signal 602_Y received byvertical polarizing antenna 601_Y and time/frequency synchronizationsignal 616, applies processing such as frequency conversion and/ororthogonal demodulation to reception signal 602_Y, and outputs basebandsignal 604_Y.

Modulated signal z1 channel fluctuation estimator 607_1 receives inputsof baseband signal 604_Y and time/frequency synchronization signal 616,performs channel estimation (calculates channel characteristics h₂₁(t))by using the reference symbol illustrated in (A) in FIG. 5, and outputschannel estimation signal 608_1.

Modulated signal z2 channel fluctuation estimator 607_2 receives inputsof baseband signal 604_Y and time/frequency synchronization signal 616,performs channel estimation (calculates channel characteristics h₂₂(t))by using the reference symbol illustrated in (B) in FIG. 5, and outputschannel estimation signal 608_2.

Time/frequency synchronizer 615 receives inputs of baseband signal 604_Xand baseband signal 604_Y, performs time synchronization (framesynchronization) and frequency synchronization by using the preamblesillustrated in (A) and (B) in FIG. 5, and outputs time/frequencysynchronization signal 616.

Control information decoder 609 receives inputs of baseband signal604_X, baseband signal 604_Y, and time/frequency synchronization signal616, performs demodulation/decoding on the control information symbolsillustrated in (A) and (B) in FIG. 5, obtains control information, andoutputs control signal 610.

Signal processor 611 receives inputs of baseband signals 604_X, 604_Y;channel estimation signals 606_1, 606_2, 608_1, 608_2; control signal610; and time/frequency synchronization signal 616, performsdemodulation/decoding on the data symbols illustrated in (A) and (B) inFIG. 5, obtains data, and outputs data 612.

Feedback information generator 613 receives inputs of baseband signal604_X, baseband signal 604_Y, and time/frequency synchronization signal616, for example, performs estimation (channel estimation) of apropagation environment by using the precoding settings training symbolsillustrated in (A) and (B) in FIG. 5, obtains a channel estimation value(channel state information (CSI)), generates feedback information basedon this, and outputs feedback signal 614 (feedback information ismediated by transmitter 618; a terminal transmits a notificationinformation symbol to the communications station as feedbackinformation).

Transmitter 618 receives as inputs feedback signal 614 and data 617, andtransmission signal 619 is output from antenna 620 as radio waves.

(Transmission Frame Configuration of Terminal)

FIG. 7 illustrates one example of a frame configuration of a modulatedsignal transmitted by a terminal. In FIG. 7, time is represented on thehorizontal axis and frequency is represented on the vertical axis. Notethat in the frequency on vertical axis, one or more carriers(subcarriers) is sufficient. Moreover, the preamble, control informationsymbol, and notification information symbol may be single-carrier (onecarrier), the data symbol may be multi-carrier, such as orthogonalfrequency-division multiplexing (OFDM). (Here, the frequency band usedto transmit a preamble, the frequency band used to transmit a controlinformation symbol, the frequency band used to transmit a notificationinformation symbol, and the frequency band used to transmit a datasymbol may be the same or may be different.) Moreover, the preamble,control information symbol, notification information symbol, and datasymbol may be multi-carrier such as OFDM. (Here, the frequency band usedto transmit a preamble, the frequency band used to transmit a controlinformation symbol, the frequency band used to transmit a notificationinformation symbol, and the frequency band used to transmit a datasymbol may be the same or may be different.) Moreover, the modulatedsignal transmitted by the terminal is not limited to a single signal(for example, a Multiple-Input Multiple-Output (MIMO) method in which aplurality of modulated signals are transmitted from a plurality ofantennas may be used, or a Multiple-Input Single-Output (MISO) methodmay be used).

The preamble illustrated in FIG. 7 is a symbol including, for example, asignal for a terminal to detect a modulated signal transmitted by acommunications station, and a signal for the terminal to performtime-synchronization or frequency-synchronization with respect to amodulated signal transmitted by a communications station.

The control information symbol illustrated in FIG. 7 is a symbol fortransmitting control information to the communications station. Thecontrol information symbol includes, for example, information on amodulation method (of a data symbol), and information on an errorcorrection code used by the terminal (encode rate, block length (codelength), etc.). The communications station obtains the controlinformation symbol and obtains information on the modulation method andinformation on the error correction code, thereby makingdemodulation/decoding of the data symbol possible.

The notification information symbol illustrated in FIG. 7 is a symbolfor “the terminal to transmit, to the communications station, a channelestimation value (CSI) obtained by, for example, the terminal performingestimation (channel estimation) of a propagation environment, which isestimated using the precoding settings training symbol transmitted bythe communications station” (accordingly, by obtaining the notificationinformation symbol, the communications station can calculate theprecoding matrix (and power change value) used to generate the datasymbol).

The reference symbol illustrated in FIG. 7 is a symbol for performingestimation (channel estimation) of a propagation environment, in orderfor the communications station to demodulate (perform wave detection on)the data symbol.

The data symbol illustrated in FIG. 7 is a symbol for transmitting data.

Note that the frame configuration illustrated in FIG. 7 of a modulatedsignal transmitted by the terminal is merely one example; symbols otherthan those illustrated in FIG. 7 may be transmitted by the terminal, andsymbols other than those illustrated in FIG. 7 may be present in theframe. Moreover, a pilot symbol for performing estimation (channelestimation) of a propagation environment may be inserted in, forexample, the control information symbol or data symbol.

(Communication State between Communications Station and Terminal)

FIG. 8 illustrates one example of a communication state between acommunications station and a terminal. Frame #1, frame #2, and frame #3are frames transmitted by the communications station, and each frame is,for example, configured as illustrated in FIG. 5. Additionally, thecommunications station transmits the frame “beacon”, and the terminaldetects the network configured by communications station by detecting“beacon”.

Frame $1 and frame $2 are frames transmitted by the terminal, and eachframe is, for example, configured as illustrated in FIG. 7.Additionally, the terminal transmits the frame “data request”.

As illustrated in FIG. 8, for example, when the communications stationcommunicates with a specific terminal, the communications stationregularly transmits the frame “beacon”.

The terminal detects the frame “beacon” transmitted by thecommunications station, and transmits the frame “data request” to thecommunications station.

The communications station receives the frame “data request” transmittedby terminal, and transmits “frame #1” including a data symbol. Notethat, as described above, “frame #1” is, for example, configured as asymbol such as the one illustrated in FIG. 5.

The terminal receives “frame #1” transmitted by the communicationsstation. Then, the terminal extracts “precoding settings trainingsymbol” included in “frame #1”, for example, performs estimation(channel estimation) of a propagation environment, and transmits thechannel estimation value (CSI) by using “notification informationsymbol” in “frame $1”.

The communications station receives “frame $1” transmitted by theterminal. Then, using “notification information symbol” included in“frame $1”, the terminal calculates parameters (a, b, θ) for performingthe precoding described in “(precoding method (1A))”, “(precoding method(1A-1))”, “(precoding method (1A-2))”, “(precoding method (1B))”,“(precoding method (1B-1))”, “(precoding method (1B-2))”. Then, upontransmission of “frame #2”, the communications station applies precodingbased on the calculated parameters to the data symbol, and transmits amodulated signal. Moreover, in “frame #2”, the communications stationtransmits “precoding settings training symbol”.

The terminal receives “frame #2” transmitted by the communicationsstation. Then, the terminal extracts “precoding settings trainingsymbol” included in “frame #2”, for example, performs estimation(channel estimation) of a propagation environment, and transmits thechannel estimation value (CSI) by using “notification informationsymbol” in “frame $2”.

The terminal receives “frame #2” transmitted by the communicationsstation. Then, the terminal extracts “precoding settings trainingsymbol” included in “frame #2”, for example, performs estimation(channel estimation) of a propagation environment, and transmits thechannel estimation value (CSI) by using “notification informationsymbol” in “frame $2”.

The communications station receives “frame $2” transmitted by theterminal. Then, using “notification information symbol” included in“frame $2”, the terminal calculates parameters (a, b, θ) for performingthe precoding described in “(precoding method (1A))”, “(precoding method(1A-1))”, “(precoding method (1A-2))”, “(precoding method (1B))”,“(precoding method (1B-1))”, “(precoding method (1B-2))”. Then, upontransmission of “frame #3”, the communications station applies precodingbased on the calculated parameters to the data symbol, and transmits amodulated signal. Moreover, in “frame #3”, the communications stationtransmits “precoding settings training symbol”.

In a communication state such as the one illustrated in FIG. 8 anddescribed above, the terminal receives “precoding settings trainingsymbol” included in “frame #(N−1)” transmitted by the communicationsstation, and the terminal generates and transmits feedback informationfrom this “precoding settings training symbol”, and the communicationsstation performs precoding of “data symbol” of “frame #N” based on thisfeedback information. Note that in the example illustrated in FIG. 8, Nis an integer greater than or equal to 2.

When the precoding method is set up as described above, thecommunications station does not hold feedback information from theterminal for setting up a preferred precoding method in “frame #1”transmitted by the communications station. In light of this, next, atransmission method such as the one illustrated in FIG. 9 will beconsidered.

(Transmission Frame Configuration of Communications Station (2))

FIG. 9 illustrates one example of a configuration of “frame #1”transmitted by the communications station illustrated in FIG. 8. Notethat description of operations in FIG. 9 that overlap with FIG. 5 willbe omitted.

FIG. 9 differs from FIG. 5 in regard to the configuration of the datasymbol (from time t3 to t4). In FIG. 9, when “data C1” is present, adata group that is identical to “data Cl”, “data C1-1”, “data C1-2”, and“data C1-3” are generated (note that, in FIG. 9, three identical datagroups are illustrated, but this example is not limiting).

The precoding method (precoding method and power change value) used totransmit “data C1-1” is precoding method #1, the precoding method usedto transmit “data C1-2” is precoding method #2, and the precoding methodused to transmit “data C1-3” is precoding method #3.

Here, precoding method #1 and precoding method #2 are different from oneanother, precoding method #1 and precoding method #3 are different fromone another, and precoding method #2 and precoding method #3 aredifferent from one another.

In other words, the precoding method used to transmit “data C1-j” isprecoding method #i, and the precoding method used to transmit “dataC1-j” is precoding method #j.

Here, when i ≠ j holds true, precoding method #i and precoding method #jare different from one another.

This makes it possible to, for example, in the example illustrated inFIG. 8, achieve an advantageous effect of an increase in the possibilityof the terminal being able to achieve a correct result with any one of“data C1-1”, “data C1-2”, or “data C1-3”.

In “(precoding method (1A))”, “(precoding method (1A-1))”, “(precodingmethod (1A-2))”, “(precoding method (1B))”, “(precoding method (1B-1))”,“(precoding method (1B-2))” described above, the precoding matrix wasdescribed as.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 35} \right\rbrack & \; \\{{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}{or}} & (35) \\\left\lbrack {{MATH}.\mspace{14mu} 36} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{{= \begin{pmatrix}{a \times \cos \; \theta} & {a \times \sin \; \theta} \\{b \times \sin \; \theta} & {{- b} \times \cos \; \theta}\end{pmatrix}},}\end{matrix} & (36)\end{matrix}$

but next a different case will be described.

(Precoding Method (2A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that 6 is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 37} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (37)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 38} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,b,{B\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (38)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 39} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}} & (39)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 40]

h ₁₁(t)×a×β×cos δ×sin θ+h ₂₂(t)×b×β×sin δ×cos θ=0   (40-1)

h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (40-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 41} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {41\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {41\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 42} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {42\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {42\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 43]

|a| ² +|b| ² =|u| ²   (43)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (2A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 44} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (44)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 45]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (45)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 46]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (46)

Precoding method determiner 316 performs the calculations described in“(precoding method (2A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 47} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {a \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {{- b} \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (47)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 48} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {48\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {48\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (2A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 49} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (49)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 50]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (50)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 51]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (51)

Precoding method determiner 316 performs the calculations described in“(precoding method (2A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 52} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}} & (52)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 53} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {53\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {53\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (2B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 54} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (54)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 55} \right\rbrack & \; \\{{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (55)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 56} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}} & (56)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 57]

h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (57-1)

h ₁₁(t)×a×β×sin δ×sin θ−h ₂₂(t)×b×β×cos δ×cos θ=0   (57-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 58} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {58\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {58\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 59} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {59\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {59\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 60]

|a| ² +|b| ² =|u| ²   (60)

(|u‥² is a parameter based on average transmitted power)

(Precoding Method (2B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 61} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (61)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 62]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (62)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 63]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (63)

Precoding method determiner 316 performs the calculations described in“(precoding method (2B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 64} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {a \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {{- b} \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (64)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 65} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {65\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {65\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (2B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 66} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (66)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 67]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (67)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 68]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (68)

Precoding method determiner 316 performs the calculations described in“(precoding method (2B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 69} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}} & (69)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 70} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {70\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {70\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (3A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 71} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (71)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 72} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (72)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 73} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (73)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 74]

−h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×h×sin δ×cos θ=0   (74-1)

h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (74-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 75} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {75\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {75\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 76} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {76\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {76\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 77]

|a| ² +|b| ² =|u| ²   (77)

(|u|² a parameter based on average transmitted power)

(Precoding Method (3A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 78} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (78)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 79]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (79)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t).

[MATH. 80]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (80)

Precoding method determiner 316 performs the calculations described in“(precoding method (3A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 81} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {{- a} \times \sin \; \theta} \\{b \times \sin \; \theta} & {b \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (81)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 82} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {82\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {82\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (3A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 83} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (83)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 84]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (84)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 85]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (85)

Precoding method determiner 316 performs the calculations described in“(precoding method (3A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 86} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}} & (86)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 87} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {87\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {87\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precolling matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (3B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 88} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (88)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 89} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (89)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 90} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (90)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 91]

h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (91-1)

−h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (91-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 92} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {92\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {92\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 93} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {93\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {93\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 94]

|a| ² |b| ² =|u| ²   (94)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (3B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 95} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (95)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 96]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (96)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 97]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (97)

Precoding method determiner 316 performs the calculations described in“(precoding method (3B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 98} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {{- a} \times \sin \; \theta} \\{b \times \sin \; \theta} & {b \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (98)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 99} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {99\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {99\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (3B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 100} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (100)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 101]

y ₁(t)=q ₁₁ ×s ₁(t)+q₁₂ ×s ₂(t)   (101)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 102]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (102)

Precoding method determiner 316 performs the calculations described in“(precoding method (3B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 103} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}} & (103)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 104} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {104\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {104\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (4A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 105} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (105)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 106} \right\rbrack} & \; \\{\mspace{79mu} {{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)}} & (106)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 107} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times \cos \; \delta \times} \\{{\sin \; \theta} - \; {{h_{22}(t)} \times b \times \beta \times}} \\{\sin \; \delta \times \cos \; \theta}\end{matrix} \\{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} & {{- {h_{11}(t)}} \times a \times \beta \times \sin \; \delta \times} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta} & {{\sin \; \theta} + \; {{h_{22}(t)} \times b \times}} \\\; & {\beta \times \cos \; \delta \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (107)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 108]

−h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (108-1)

h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (108-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 109} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {109\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {109\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 110} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {110\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {110\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 111]

|a| ² +|b| ² =|u| ²   (111)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (4A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 112} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (112)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 113]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (113)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 114]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (114)

Precoding method determiner 316 performs the calculations described in“(precoding method (4A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 115} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {{- a} \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {b \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (115)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 116} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {116\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {116\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (4A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 117} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (117)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 118]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (118)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 119]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (119)

Precoding method determiner 316 performs the calculations described in“(precoding method (4A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 120} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} & (120)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 121} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {121\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {121\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (4B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 122} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (122)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 123} \right\rbrack} & \; \\{\mspace{79mu} {{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)}} & (123)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 124} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times} \\{{\sin \; \theta} - \; {{h_{22}(t)} \times b \times}} \\{\beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} & {{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta} & {{\sin \; \theta} + \; {{h_{22}(t)} \times b \times}} \\\; & {\beta \times \cos \; \delta \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (124)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 125]

h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (125-1)

−h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (125-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 126} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {126\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {126\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 127} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {127\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {127\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 128]

|a| ² +|b| ² =|u| ²   (128)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (4B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 129} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (129)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 130]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (130)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 131]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (131)

Precoding method determiner 316 performs the calculations described in“(precoding method (4B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 132} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {{- a} \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {b \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (132)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 133} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {133\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {133\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (4B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 134} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (134)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 135]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (135)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 136]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (136)

Precoding method determiner 316 performs the calculations described in“(precoding method (4B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 137} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} & (137)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 138} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {138\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {138\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (5A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 139} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (139)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 140} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (140)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 141} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \cos \; \delta \times} \\{{\cos \; \theta} - \; {{h_{22}(t)} \times b \times}} \\{\sin \; \delta \times \sin \; \theta}\end{matrix} \\{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} & {{- {h_{11}(t)}} \times a \times \sin \; \delta \times} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta} & {{\cos \; \theta} + \; {{h_{22}(t)} \times b \times}} \\\; & {\cos \; \delta \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (141)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 142]

−h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (142-1)

h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (142-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 143} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {143\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {143\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 144} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {144\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {144\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 145]

|a| ² +|b| ² =|u| ²   (145)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (5A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 146} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (146)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 147]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (147)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 148]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (148)

Precoding method determiner 316 performs the calculations described in“(precoding method (5A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 149} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {{- a} \times \cos \; \theta} \\{b \times \cos \; \theta} & {b \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (149)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 150} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {150\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {150\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (5A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 151} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (151)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 152]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (152)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(0).

[MATH. 153]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (153)

Precoding method determiner 316 performs the calculations described in“(precoding method (5A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 154} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}} & (154)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 155} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {155\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {155\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (5B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 156} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (156)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 157} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (157)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 158} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \cos \; \delta \times} \\{{\cos \; \theta} - \; {{h_{22}(t)} \times b \times}} \\{\sin \; \delta \times \sin \; \theta}\end{matrix} \\{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} & {{- {h_{11}(t)}} \times a \times \sin \; \delta \times} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta} & {{\cos \; \theta} + \; {{h_{22}(t)} \times b \times}} \\\; & {\cos \; \delta \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (158)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 159]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (159-1)

−h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (159-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 160} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {160\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {160\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates 74 , a, and b fromthe feedback information from the terminal so that the following istrue.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 161} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {161\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {161\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 162]

|a| ² +|b| ² =|u| ²   (162)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (5B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 163} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (163)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 164]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (164)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 165]

z ₂(t)=q ₂₁ ×s ₁(t)+q₂₂ ×s ₂(t)   (165)

Precoding method determiner 316 performs the calculations described in“(precoding method (5B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 166} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {{- a} \times \cos \; \theta} \\{b \times \cos \; \theta} & {b \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (166)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 167} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {167\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {167\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (5B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 168} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (168)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 169]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (169)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 170]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (170)

Precoding method determiner 316 performs the calculations described in“(precoding method (5B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 171} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}} & (171)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 172} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {172\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {172\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (6A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 173} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (173)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 174} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (174)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 175} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} & {{{- {h_{11}(t)}} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (175)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 176]

−h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (176-1)

h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (176-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 177} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {177\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {177\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 178} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {178\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {178\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 179]

|a| ² +|b| ² =|u| ²   (179)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (6A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 180} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (180)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 181]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (181)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 182]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (182)

Precoding method determiner 316 performs the calculations described in“(precoding method (6A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 183} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {{- a} \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {b \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (183)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 184} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {184\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {184\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (6A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 185} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (185)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 186]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (186)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 187]

y ₂(t)=q ₂₁ ×s ₁(t)+q₂₂ ×s ₂(t)   (187)

Precoding method determiner 316 performs the calculations described in“(precoding method (6A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 188} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}} & (188)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 189} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {189\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {189\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (6B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 190} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (190)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 191} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,b,{B\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {{numbers}\text{}\left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}}} \right)} & (191)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 192} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (192)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 193]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (193-1)

−h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (193-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 194} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {194\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {194\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 195} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {195\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {195\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 196]

|a| ² +|b| ² =|u| ²   (196)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (6B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 197} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (197)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 198]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (198)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 199]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (199)

Precoding method determiner 316 performs the calculations described in“(precoding method (6B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 200} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {{- a} \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {b \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (200)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 201} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {201\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {201\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (6B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 202} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (202)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 203]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (203)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 204]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (204)

Precoding method determiner 316 performs the calculations described in“(precoding method (6B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 205} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}} & (205)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 206} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {206\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {206\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (7A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 207} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (207)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 208} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (208)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 209} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \; \sin \; \theta} -} & {{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta} \\{{{h_{11}(t)} \times a \times \sin \; \delta \times \; \sin \; \theta} +} & {{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (209)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 210]

h ₁₁(t)×a×cos δ×cos θ+h ₂₂(t)×b×sin δ×sin θ=0   (210-1)

h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (210-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 211} \right\rbrack & \; \\{{b = {\frac{h_{12}(t)}{h_{22}(t)} \times a}}{and}} & \left( {211\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {211\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 212} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {212\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {212\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 213]

|a| ² +|b| ² =|u| ²   (213)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (7A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 214} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (214)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 215]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (215)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 216]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (216)

Precoding method determiner 316 performs the calculations described in“(precoding method (7A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 217} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {a \times \cos \; \theta} \\{b \times \cos \; \theta} & {{- b} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (217)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 218} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{21}(t)} \times a}}{and}} & \left( {218\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {218\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (7A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 219} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (219)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 220]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (220)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 221]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (221)

Precoding method determiner 316 performs the calculations described in“(precoding method (7A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 222} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}} & (222)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 223} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {223\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {223\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (7B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 224} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (224)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 225} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (225)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 226} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \; \sin \; \theta} -} & {{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta} \\{{{h_{11}(t)} \times a \times \sin \; \delta \times \; \sin \; \theta} +} & {{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (226)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 227]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (227-1)

h ₁₁(t)×a×sin δ×sin θ−h ₂₂(t)×b×cos δ×cos θ=0   (227-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 228} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {228\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {228\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 229} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {229\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {229\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 230]

|a| ² +|b| ² =|u| ²   (230)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (7B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 231} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} & (231)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 232]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (232)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 233]

z ₂(t)=q ₂₁ ×s ₁(t)+q₂₂ ×s ₂(t)   (233)

Precoding method determiner 316 performs the calculations described in“(precoding method (7B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 234} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {a \times \cos \; \theta} \\{b \times \cos \; \theta} & {{- b} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (234)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 235} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {235\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {235\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precolling Method (7B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 236} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} & (236)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 237]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (237)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 238]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (238)

Precoding method determiner 316 performs the calculations described in“(precoding method (7B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 239} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}} & (239)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 240} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {240\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {240\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (8A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 241} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (241)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 242} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,b,{B\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (242)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 243} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}} & (243)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 244]

h ₁₁(t)×a×β×cos δ×cos θ+h ₂₂(t)×b×β×sin δ×sin θ=0   (244-1)

h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (244-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 245} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {245\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {245\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 246} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {246\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {246\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 247]

|a| ² +|b| ² =|u| ²   (247)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (8A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 248} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} & (248)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 249]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (249)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 250]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (250)

Precoding method determiner 316 performs the calculations described in“(precoding method (8A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 251} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {a \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {{- b} \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (251)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 252} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {252\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {252\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (8A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 253} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22\;}\end{pmatrix} & (253)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 254]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (254)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 255]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (255)

Precoding method determiner 316 performs the calculations described in“(precoding method (8A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 256} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}} & (256)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 257} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {257\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {257\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (8B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 258} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (258)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 259} \right\rbrack} & \; \\{\mspace{79mu} {{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)}} & (259)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 260} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} - {{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}} \\{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} + \; {{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} + {{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}} \\{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} - \; {{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (260)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 261]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (261-1)

h ₁₁(t)×a×β×sin δ×cos θ−h₂₂(t)×b×β×cos δ×sin θ=0   (261-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 262} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {262\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {262\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 263} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {263\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {263\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 264]

|a| ² +|b| ² =|u| ²   (264)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (8B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 265} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (265)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 266]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (266)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 267]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (267)

Precoding method determiner 316 performs the calculations described in“(precoding method (8B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 268} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {a \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {{- b} \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (268)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 269} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {269\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {269\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (8B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 270} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (270)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 271]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (271)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 272]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (272)

Precoding method determiner 316 performs the calculations described in“(precoding method (8B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 273} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}} & (273)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 274} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {274\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {274\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (9A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 275} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (275)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 276} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,b,{{are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (276)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 277} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega \; + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \; e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \; e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \; e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \; e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (277)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 278]

h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×sin θ+h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×cos θ=0  (278-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×cos θ+h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0   (278-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 279} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {279\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {279\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 280} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {280\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {280\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 281]

|a| ² +|b| ² =|u| ²   (281)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (9A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 282} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (282)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 283]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (283)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t).

[MATH. 284]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (284)

Precoding method determiner 316 performs the calculations described in“(precoding method (9A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 285} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega \; + \lambda})}}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {a \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (285)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 286} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {286\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {286\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (9A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 287} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (287)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 288]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (288)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 289]

y ₂(t)=q ₂₁ ×s ₁(t)30 q ₂₂ ×s ₂(t)   (289)

Precoding method determiner 316 performs the calculations described in“(precoding method (9A))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 290} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega \; + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} & (290)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 291} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {291\text{-}1} \right) \\{and} & \; \\{{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}}\mspace{14mu}} & \left( {291\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (9B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 292} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (292)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 293} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega \; + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (293)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 294} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega \; + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \; e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \; e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \; e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \; e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (294)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 295]

h ₁₁(t)×a×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×e ^(jω)×sin δ×sin θ=0   (295-1)

h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×sin θ−h ₂₂(t)×b×3 ^(j(ω−λ))×cos δ×cos θ=0  (295-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 296} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {296\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {296\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 297} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {297\text{-}1} \right) \\{and} & \; \\{{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}}\mspace{14mu}} & \left( {297\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 298]

|a| ² +|b| ² =|u| ²   (298)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (9B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 299} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (299)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 300]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (300)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 301]

i z₂(t)=q ₂₁ ×s ₁(t)+q₂₂ ×s ₂(t)   (301)

Precoding method determiner 316 performs the calculations described in“(precoding method (9B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 302} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega \; + \lambda})}}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {a \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (302)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 303} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {303\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {303\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (9B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 304} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (304)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 305]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (305)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 306]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (306)

Precoding method determiner 316 performs the calculations described in“(precoding method (9B))” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 307} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} & (307)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 308} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {308\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {308\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (10A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 309} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (309)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, n, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 310} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (310) \\{\mspace{76mu} \left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 311} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \; \beta \times e^{j\; \mu} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \; \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \; \beta \times e^{j\; \mu} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \; \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (311)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 312]

h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×sin θh ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×cos θ=0  (312-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×cos θ+h₂₂(t)×b×β×e ^(jω)×cos δ×sin θ=0  (312-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 313} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {313\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {313\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 314} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {314\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radian}}}} & \left( {314\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 315]

|a| ² +|b| ² =|u| ²   (315)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (10A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 316} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (316)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 317]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (317)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 318]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (318)

Precoding method determiner 316 performs the calculations described in“(precoding method (10A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 319} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {a \times \beta \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times \beta \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (319)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 320} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {320\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {320\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (10A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 321} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (321)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 322]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (322)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 323]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (323)

Precoding method determiner 316 performs the calculations described in“(precoding method (10A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 324} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \; + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \; + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (324)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 325} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {325\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {325\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (10B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 326} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (326)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 327} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (327) \\{\mspace{79mu} \left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 328} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (328)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 329]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×sin θ=0  (329-1)

h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×sin θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×cosθ=0   (329-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 330} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {330\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {330\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 331} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {331\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {331\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 332]

|a| ² +|b| ² =|u| ²   (332)

(|u|² is a parameter based on average transmited power)

(Precoding Method (10B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 333} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (333)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 334]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (324)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 335]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (335)

Precoding method determiner 316 performs the calculations described in“(precoding method (10B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 336} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (336)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 337} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {337\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {337\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (10B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 338} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (338)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 339]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (329)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 340]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (340)

Precoding method determiner 316 performs the calculations described in“(precoding method (10B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 341} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (341)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 342} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {342\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {342\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (11A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 343} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (343)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 344} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (344) \\{\,\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 345} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (345)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 346]

−h ₁₁(t)×a×e ^(h(μ+λ))×cos δ×sin θ−h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×cos θ=0  (346-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×cos θ+h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0   (346-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 347} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{11mu} \times e^{j{({\mu - \omega})}}\; {and}}} & \left( {347\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {347\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 348} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{11mu} \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {348\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {348\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 349]

|a| ² +|b| ² =|u| ²   (349)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (11A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 350} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (350)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 351]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (351)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 352]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (352)

Precoding method determiner 316 performs the calculations described in“(precoding method (11A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 353} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (353)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 354} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{11mu} \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {354\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {354\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (11A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 355} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (355)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 356]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (356)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 357]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (357)

Precoding method determiner 316 performs the calculations described in“(precoding method (11A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 358} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (358)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 359} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{11mu} \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {359\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {359\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (11B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 360} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (360)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 361} \right\rbrack & \; \\{{\begin{pmatrix}{Z_{1}(t)} \\{Z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}}\left( {a,b,{{are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (361)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 362} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} - {{h_{22}(t)} \times}} \\{b \times e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} - \; {{h_{22}(t)} \times b \times}} \\{e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\{{h_{11}(t)} \times a \times e^{j\; \mu} \times} & {{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} + {{h_{22}(t)} \times}} & {{\sin \; \delta \times \sin \; \theta} +} \\{b \times e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta} & {\; {{h_{22}(t)} \times b \times}} \\\; & {e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (362)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 363]

h ₁₁(t)×a×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×e ^(jω)×sin δ×sin θ=0   (363-1)

−h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×sin θ+h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×cos θ=0  (363-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 364} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{11mu} \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {364\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {364\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 365} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{11mu} \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {365\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {365\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 366]

|a| ² +|b| ² =|u| ²   (366)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (11B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 367} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (367)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 368]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (368)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 369]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (369)

Precoding method determiner 316 performs the calculations described in“(precoding method (11B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 370} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (370)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 371} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {371\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {371\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (11B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 372} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (372)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 373]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (373)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 374]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (374)

Precoding method determiner 316 performs the calculations described in“(precoding method (11B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 375} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (375)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 376} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {376\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {376\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (12A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 377} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\; \cos \; \delta} & {{- {h_{22}(t)}}\; \sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (377)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3/π2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 378} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (378) \\{\mspace{79mu} \left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 379} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (379)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 380]

−h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×sin θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×cosθ=0   (380-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×cos θ+h ₂₂(t)×b×β×e ^(jω)×cos δ×sin θ=0  (380-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 381} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {381\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {381\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

[MATH.  382] $\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {382\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {382\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 383]

|a| ² +|b| ² =|u| ²   (383)

(|μ|² is a parameter based on average transmitted power)

(Precoding Method (12A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 384} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (384)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 385]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ +s ₂(t)   (385)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 386]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (386)

Precoding method determiner 316 performs the calculations described in“(precoding method (12A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 387} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (387)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 388} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {388\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {388\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (12A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 389} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (389)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 390]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (390)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 391]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ +s ₂(t)   (391)

Precoding method determiner 316 performs the calculations described in“(precoding method (12A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 392} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (392)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 393} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {393\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {393\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (12B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 394} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (394)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 395} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (395) \\{\mspace{79mu} \left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 396} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (396)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 397]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×sin θ=0  (397-1)

−h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×sin θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×cosθ=0   (397-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 398} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {398\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {398\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 399} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {399\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {399\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 400]

|a| ² +|b| ² +|u| ²   (400)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (12B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 401} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (401)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 402]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (402)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 403]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (403)

Precoding method determiner 316 performs the calculations described in“(precoding method (12B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 404} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times \beta \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {b \times \beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (404)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 405} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {405\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {405\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (12B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 406} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (406)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 407]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (407)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 408]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ +s ₂(t)   (408)

Precoding method determiner 316 performs the calculations described in“(precoding method (12B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 409} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (409)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 410} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {410\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {410\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (13A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 411} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (411)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 412} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (412) \\\left( {a,{b\mspace{20mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right) & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 413} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times s\; {in}\; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (413)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 414]

−h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×sin θ=0  (414-1)

h ₁₁(t)×a×e ^(jμ) sin δ×sin θ+h ₂₂(t)+b×e ^(jω)×cos δ×cos θ=0   (414-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 415} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {415\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {415\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 416} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {416\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {416\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 417]

|a| ² |b| ² +|u| ²   (417)

(|u|² is a parameter basad on average transmittad power)

(Precoding Method (13A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 418} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (418)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 419]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (419)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 420]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (420)

Precoding method determiner 316 performs the calculations described in“(precoding method (13A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 421} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (421)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 422} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {422\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {422\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (13A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 423} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (423)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 424]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (424)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 425]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (425)

Precoding method determiner 316 performs the calculations described in“(precoding method (13A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 426} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (426)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 427} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {427\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {427\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (13B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 428} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (428)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 429} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (429) \\\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right. & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{11mu} 430} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times s\; {in}\; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (430)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 431]

h ₁₁(t)×a×e ^(jμ) cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (431-1)

−h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ+h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (431-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 432} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {432\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {432\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 433} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {433\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {433\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 434]

|a| ² +|b| ² +|u| ²   (434)

(|μ|² is a parameter based on average transmitted power)

(Precoding Method (13B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 435} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (435)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 436]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (436)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 437]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (437)

Precoding method determiner 316 performs the calculations described in“(precoding method (13B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 438} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times e^{j{({\mu \mspace{11mu} + \mspace{11mu} \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {b \times e^{j{({\omega \mspace{11mu} + \mspace{11mu} \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (438)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 439} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {439\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {439\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (13B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 440} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (440)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 441]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (441)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 442]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (442)

Precoding method determiner 316 performs the calculations described in“(precoding method (13B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 443} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (443)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 444} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {444\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {444\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (14A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 445} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (445)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 446} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu \; + \; \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega \; + \; \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (446) \\{\mspace{79mu} \left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 447} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu \; + \; \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega \; + \; \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \; \beta \times e^{j\; \mu}\cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \; \beta \times e^{j{({\mu \; + \; \lambda})}} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j{({\omega \; + \; \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \; \beta \times e^{j\; \mu}\sin \; \delta \times s\; {in}\; \theta} +} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \; \beta \times e^{j{({\mu \; + \; \lambda})}} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \; \beta \times e^{j{({\omega \; + \; \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (447)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 448]

−h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×sinθ=0   (448-1)

h ₁₁(t)×a×β×e ^(jμ) sin δ×sin θ+h ₂₂(t)×b×β×e ^(jω)+×cos δ×cos θ=0  (448-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 449} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {449\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {449\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 450} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {450\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {450\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 451]

|a| ² +|b| ² =|u| ²   (451)

(|μ|² is a parameter based on average transmitted power)

(Precoding Method (14A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 452} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (452)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 453]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (453)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 454]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (454)

Precoding method determiner 316 performs the calculations described in“(precoding method (14A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 455} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu \; + \; \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega \; + \; \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times \beta \times e^{j{({\mu \; + \; \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {b \times \beta \times e^{j{({\omega \; + \; \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (455)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 456} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {456\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {456\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (14A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 457} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (457)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 458]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (458)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 459]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (459)

Precoding method determiner 316 performs the calculations described in“(precoding method (14A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 460} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (460)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 461} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {461\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {461\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (14B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 462} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (462)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 463} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (463) \\{\mspace{79mu} \left( {a,b,{\beta \mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{11mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 464} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times s\; {in}\; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (464)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 465]

h ₁₁(t)×a×β×e ^(jμ) cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×cos θ=0  (465-1)

−h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×sinθ=0   (465-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 466} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {466\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {466\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 467} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {467\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {467\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 468]

|a| ² +|b| ² =|u| ²   (468)

(|u|² is a parameter based an average transmitted power)

(Precoding Method (14B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 469} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (469)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 470]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₁(t)   (470)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 471]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (471)

Precoding method determiner 316 performs the calculations described in“(precoding method (14B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 472} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (472)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 473} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {473\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {473\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (14B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 474} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (474)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 475]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (475)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 476]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (476)

Precoding method determiner 316 performs the calculations described in“(precoding method (14B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 477} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (477)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 478} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {478\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {478\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (15A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 479} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (479)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\; \left\lbrack {{MATH}.\mspace{14mu} 480} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (480) \\\left( {a,b,{{are}\mspace{14mu} {complex}\mspace{14mu} {{numbers}{\; \mspace{11mu}}\left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}}} \right) & \;\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 481} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times s\; {in}\; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (481)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 482]

h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×cos θ+h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×sin θ=0  (482-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×e ^(jω)×cos δ×cos θ=0   (482-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 483} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {483\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {483\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 484} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {484\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {484\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 485]

|a| ² +|b| ² =|u| ²   (485)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (15A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 486} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (486)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 487]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (487)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 488]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (488)

Precoding method determiner 316 performs the calculations described in“(precoding method (15A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 489} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {e^{j{({\mu + \lambda})}} \times \cos \mspace{14mu} \theta} \\{e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {a \times e^{j{({\mu + \lambda})}} \times \cos \mspace{14mu} \theta} \\{b \times e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \sin \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (489)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 490} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {490\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {490\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (15A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 491} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (491)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 492]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (492)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 493]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (493)

Precoding method determiner 316 performs the calculations described in“(precoding method (15A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 494} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {e^{j{({\mu + \lambda})}} \times \cos \mspace{14mu} \theta} \\{e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \mspace{14mu} \theta}\end{pmatrix}} & (494)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 495} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {495\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {495\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (15B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 496} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (496)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 497} \right\rbrack & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {e^{j\; {({\mu + \lambda})}} \times \cos \mspace{14mu} \theta} \\{e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\left( {a,{b\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}\mspace{14mu} {numbers}} \right)}} \right)} & (497)\end{matrix}$

In this case, the following equation holds true.

     [MATH.  498]                                           (498)$\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}} \times \sin \mspace{14mu} \delta} \\{{h_{11}(t)} \times \sin \mspace{14mu} \delta} & {{h_{22}(t)} \times \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}} \times \sin \mspace{14mu} \delta} \\{{h_{11}(t)} \times \sin \mspace{14mu} \delta} & {{h_{22}(t)} \times \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {e^{j\; {({\mu \; + \; \lambda})}} \times \cos \mspace{14mu} \theta} \\{e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- e^{j\; {({\omega \; + \; \lambda})}}} \times \sin \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times e^{j\mu} \times \cos \mspace{14mu} \delta \times \sin \mspace{14mu} \theta} -} \\{{h_{22}(t)} \times b \times e^{j\omega} \times \sin \mspace{14mu} \delta \times \cos \mspace{14mu} \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times e^{j{({\mu \; + \; \lambda})}} \times \cos \mspace{14mu} \delta \times \cos \mspace{14mu} \theta} +} \\{{h_{22}(t)} \times b \times e^{j{({\omega \; + \; \lambda})}} \times \sin \mspace{14mu} \delta \times \sin \mspace{14mu} \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times e^{j\mu} \times \sin \mspace{14mu} \delta \times \sin \mspace{14mu} \theta} +} \\{{h_{22}(t)} \times b \times e^{j\omega} \times \cos \mspace{14mu} \delta \times \cos \mspace{14mu} \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times e^{j{({\mu \; + \; \lambda})}} \times \sin \mspace{14mu} \delta \times \cos \mspace{14mu} \theta} -} \\{{h_{22}(t)} \times b \times e^{j{({\omega \; + \; \lambda})}} \times \cos \mspace{14mu} \delta \times \sin \mspace{14mu} \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 499]

h ₁₁(t)×a×e ^(jμ) cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (499-1)

h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (499-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 500} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {500\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {500\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 501} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {501\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {501\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 502]

|a| ² +|b| ² =|u| ²   (502)

(|u|² is a parameter based on average trmsmitted power)

(Precoding Method (15B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 503} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (503)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 504]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (504)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 505]

z ₂(t)=q ₂₁ ×s ₁(t)+q₂₂ ×s ₂(t)   (505)

Precoding method determiner 316 performs the calculations described in“(precoding method (15B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 506} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {e^{j{({\mu + \lambda})}} \times \cos \mspace{14mu} \theta} \\{e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \mspace{14mu} \theta} & {a \times e^{j{({\mu + \lambda})}} \times \cos \mspace{14mu} \theta} \\{b \times e^{j\; \omega} \times \cos \mspace{14mu} \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \sin \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (506)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 507} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {507\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {507\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (15B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 508} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (508)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 509]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (509)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 510]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (510)

Precoding method determiner 316 performs the calculations described in“(precoding method (15B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 511} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j\; {({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} & (511)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 512} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {512\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {512\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (16A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 513} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (513)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 514} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (514)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 515} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (515)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 516]

h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×cos θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×sinθ=0   (516-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×β×e ^(jω)×cos δ×cos θ=0  (516-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 517} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {517\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {\frac{\pi}{2} \times n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {517\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 518} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {518\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {\frac{\pi}{2} \times n\; \pi \mspace{14mu} {radians}}}} & \left( {518\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 519]

|a| ² +|b| ² =|u| ²   (519)

(↑u|² is a parameter based on avarage tramsmitted power)

(Precoding Method (16A-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 520} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (520)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 521]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (521)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 522]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (522)

Precoding method determiner 316 performs the calculations described in“(precoding method (16A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 523} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times \beta \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (523)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 524} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {524\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {\frac{\pi}{2} \times n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {524\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (16A-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 525} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (525)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 526]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (526)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 527]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (527)

Precoding method determiner 316 performs the calculations described in“(precoding method (16A))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 528} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (528)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 529} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {529\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {\frac{\pi}{2} \times n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {529\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Precoding Method (16B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device (for example, a terminal) can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 530} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (530)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 531} \right\rbrack} & \; \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}}\mspace{20mu} \left( {a,b,{B\mspace{14mu} {are}\mspace{14mu} {complex}\mspace{14mu} {numbers}\mspace{14mu} \left( {{may}\mspace{14mu} {be}\mspace{14mu} {actual}{\mspace{11mu} \;}{numbers}} \right)}} \right)} & (531)\end{matrix}$

In this case, the following equation holds true.

$\begin{matrix}{\left\lbrack {{MATH}.\mspace{14mu} 532} \right\rbrack \mspace{11mu}} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (532)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 533]

h ₁₁(t)×a×β×e ^(jμ) cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×cos θ=0  (532-1)

h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×sinθ=0   (532-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 534} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {534\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {534\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 535} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {535\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {535\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 536]

|a| ² +|b| ² =|u| ²   (536)

(|u|² is a parameter based on average transmitted power)

(Precoding Method (16B-1))

FIG. 3 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 3 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isz₁(t), and weighted signal 307B output by weighting synthesizer 306B isz₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 537} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (537)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 538]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (538)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 539]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (539)

Precoding method determiner 316 performs the calculations described in“(precoding method (16B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 540} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times \beta \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (540)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 541} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {541\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {541\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (16B-2))

FIG. 4 illustrates a configuration of a communications station differentfrom the communications station illustrated in FIG. 3. One example ofprocesses performed by weighting synthesizers 306A, 306B, coefficientmultipliers 401A, 401B, and precoding method determiner 316 illustratedin FIG. 4 will be described.

Mapped signal 305A output by mapper 304A is s₁(t), and mapped signal305B output by mapper 304B is s₂(t).

Moreover, weighted signal 307A output by weighting synthesizer 306A isy₁(t), and weighted signal 307B output by weighting synthesizer 306B isy₂(t).

Furthermore, coefficient multiplied signal 402A output by coefficientmultiplier 401A is z₁(t), and coefficient multiplied signal 402B outputby coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 542} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (542)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 543]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×s ₂(t)   (543)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 544]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×s ₂(t)   (544)

Precoding method determiner 316 performs the calculations described in“(precoding method (16B))” based on feedback information from aterminal, and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 545} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (545)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 546} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {546\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {546\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precolling matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 4 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 4 receives an input ofweighted signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), and outputscoefficient multiplied signal 402B (z₂(t)).

(Communications Station Configuration (3))

Communications station configurations different from the configurationsillustrated in FIG. 2 and FIG. 3 are illustrated in FIG. 10 and FIG. 11.Operations that are the same as in FIG. 2 and FIG. 3 share likereference marks. The configurations illustrated in FIG. 10 and FIG. 11differ from the configurations illustrated in FIG. 2 and FIG. 3 in thatphase changer 1001B is added between mapper 304B and weightingsynthesizer 306B.

Phase changer 1001B receives inputs of mapped signal 305B andtransmission method/frame configuration signal 319, changes the phase ofmapped signal 305B based on transmission method/frame configurationsignal 319, and outputs phase-changed signal 1002B.

Note that in FIG. 10 and FIG. 11, weighting synthesizer 306B performsprocessing on phase-changed signal 1002B as an input instead of mappedsignal 305B.

(Polarized MIMO System)

In the example illustrated in FIG. 1, the following relation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 547} \right\rbrack & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} & (547)\end{matrix}$

Then, in a polarized Multiple-Input Multiple Output (MIMO) system, whenthe cross polarization discrimination (XPD) is a large value, h₁₂(t) andh₂₁(t) can be treated as h₁₂(t)≈0 and h₂₁(t)≈0. Then, when themillimeter waveband is used, since the radio waves have strong straighttravelling properties, there is a high probability of the followingcircumstance.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 548} \right\rbrack & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} & (548)\end{matrix}$

Here, if z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), mapped baseband signal s₁(t) is not affected(interference) by mapped baseband signal s₂(t), and thus achievingfavorable data reception quality is likely. Similarly, since mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t), achieving favorable data reception quality is likely.

However, h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t) are complex numbers (may beactual numbers). r₁(t), r₂(t), z₁(t), and z₂(t) are complex numbers (maybe actual numbers). n₁(t) and n₂(t) are noise, and are complex numbers.

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 549} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (549)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

The previous descriptions were in regard to a method of switching theprecoding method by the communications station based on feedbackinformation from a terminal.

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, insuch a state, application of a precoding method that can ensure datareception quality even when fluctuation in the antenna state ismoderate—just like the precoding methods described hereinbeforeisdesirable. Hereinafter, a precoding method that satisfies these will bedescribed.

(Precoding Method (17A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 550} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (550)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 551} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \delta} & {\sin \; \delta} \\{\sin \; \delta} & {{- \cos}\; \delta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (551)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 552} \right\rbrack \mspace{11mu}} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (552)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 553]

h ₁₁(t)×a×cos δ×sin θ+h ₂₂(t)×b×sin δ×cos θ=0   (553-1)

h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (553-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 554} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {554\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {554\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 555} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & (555) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {555\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 556]

|a| ² +|b| ² =|u| ²   (556)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (17A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 557} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (557)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 558]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (558)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 559]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (559)

Precoding method determiner 316 performs the calculations described in“(precoding method (17A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 560} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {\sin \mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {{- \cos}\mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \mspace{14mu} \theta} & {a \times \sin \mspace{14mu} \theta} \\{b \times \sin \mspace{14mu} \theta} & {{- b} \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (560)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated.

Here, based on feedback information from a terminal, precoding methoddeterminer 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 561} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {561\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {561\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (17A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 562} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (562)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 563]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (563)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 564]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (564)

Precoding method determiner 316 performs the calculations described in“(precoding method (17A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 565} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \mspace{14mu} \theta} & {\sin \mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {{- \cos}\mspace{14mu} \theta}\end{pmatrix}} & (565)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 566} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {566\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {566\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (17A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 567} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (567)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (17A)” is not satisfied.

(Precoding Method (17B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 568} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (568)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 569} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {\sin \mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {{- \cos}\mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (569)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

     [MATH.  570]                                           (570)$\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{s_{1}(t)} \\\begin{matrix}e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{matrix}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 571]

h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (571-1)

h ₁₁(t)×a×sin δ×sin θ−h ₂₂(t)×b×cos δ×cos θ=0   (571-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 572} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {572\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {572\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 573} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {573\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {573\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 574]

|a| ² +|b| ² =|u| ²   (574)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (17B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 575} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (575)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 576]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (576)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 577]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (577)

Precoding method determiner 316 performs the calculations described in“(precoding method (17B)” based on feedback information from a terminal,and determines the precoding matrix.

[MATH.  578] $\begin{matrix}\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {\sin \mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {{- \cos}\mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \mspace{14mu} \theta} & {a \times \sin \mspace{14mu} \theta} \\{b \times \sin \mspace{14mu} \theta} & {{- b} \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (578)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

[MATH.  579] $\begin{matrix}{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {579\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {579\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (17B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

[MATH.  580] $\begin{matrix}\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (580)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 581]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (581)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 582]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (582)

Precoding method determiner 316 performs the calculations described in“(precoding method (17B)” based on feedback information from a terminal,and determines the precoding matrix.

[MATH.  583] $\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \mspace{14mu} \theta} & {\sin \mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {{- \cos}\mspace{14mu} \theta}\end{pmatrix}} & (583)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

[MATH.  584] $\begin{matrix}{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {584\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {584\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (17B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

[MATH.  585] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} =} & {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{=} & {\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \right.} \\ & {{\left. {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (585)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (17B)” is not satisfied.

(Precoding Method (18A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

[MATH.  586] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\sin \mspace{14mu} \delta} \\{{h_{11}(t)}\sin \mspace{14mu} \delta} & {{h_{22}(t)}\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (586)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

     [MATH.  587] $\begin{matrix}{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(i)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (587)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

[MATH.  588] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{12}(t)}} \times \sin \; \delta} \\{{h_{21}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{12}(t)}} \times \sin \; \delta} \\{{h_{21}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\Delta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(i)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} & {{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times {\beta sin}\; \delta \times \sin \; \theta} & {{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta} \\{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} & {{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta} & {{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{1}(t)}}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (588)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 589]

h ₁₁(t)×a×β×cos δ×sin θ+h ₂₂(t)×b×β×sin δ×cos θ=0   (589-1)

h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (589-2)

Accordingly, it is sufficient if the following holds true.

[MATH.  590] $\begin{matrix}{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {590\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {590\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

[MATH.  591] $\begin{matrix}{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {591\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {591\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 592]

|a| ² +|b| ² =|u| ²   (592)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (18A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

[MATH.  593] $\begin{matrix}\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (593)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 594]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (594)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 595]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ +e ^(jγ(t)) ×s ₂(t)   (595)

Precoding method determiner 316 performs the calculations described in“(precoding method (18A)” based on feedback information from a terminal,and determines the precoding matrix.

[MATH.  596] $\begin{matrix}\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \mspace{14mu} \theta} & {a \times \beta \times \sin \mspace{14mu} \theta} \\{b \times \beta \times \sin \mspace{14mu} \theta} & {{- b} \times \beta \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (596)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

[MATH.  597] $\begin{matrix}{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {597\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {597\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (18A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

[MATH.  598] $\begin{matrix}\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (598)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 599]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (599)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 600]

y ₂(t)=q ₂₁ +s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (600)

Precoding method determiner 316 performs the calculations described in“(precoding method (18A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 601} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}} & (601)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 602} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {602\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {602\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (18A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 603} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + \sqrt{\frac{1}{K + 1}}} \right.} \\{{\left. \begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (603)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of hx_(y)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (18A)” is not satisfied.

(Precoding Method (18B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 604} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (604)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 605} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}} & (605)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 606} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} - {{h_{22}(t)} \times}} \\{b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} + {{h_{22}(t)} \times}} \\{b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} + {{h_{22}(t)} \times}} \\{b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} - {{h_{22}(t)} \times}} \\{b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{S_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{S_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (606)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 607]

h ₁₁(t)×a×βcos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (607-1)

h ₁₁(t)×a×β×sin δ×sin θ−h ₂₂(t)×b×β×cos δ×cos θ=0   (607-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 608} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {608\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{11mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {608\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 609} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {609\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {609\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 610]

|a| ² +|b| ^(b) =|u| ²   (610)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (18B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 611} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (611)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 612]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (612)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 613]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (613)

Precoding method determiner 316 performs the calculations described in“(precoding method (18B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 614} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {a \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {{- b} \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (614)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 615} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {615\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{11mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {615\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (18B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 616} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (616)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 617]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (617)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 618]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (618)

Precoding method determiner 316 performs the calculations described in“(precoding method (18B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 619} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}} & (619)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 620} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {620\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{11mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {620\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (18B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 621} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + \sqrt{\frac{1}{K + 1}}} \right.} \\{{\left. \begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (621)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (18B)” is not satisfied.

(Precoding Method (19A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 622} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (622)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 623} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (623)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 624} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (624)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 625]

−h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (625-1)

h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (625-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 626} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {626\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {626\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 627} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {627\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {627\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 628]

|a| ² +|b| ² =|u| ²   (628)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (19A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 629} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (629)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 630]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (630)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 631]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (631)

Precoding method determiner 316 performs the calculations described in“(precoding method (19A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 633} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {633\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {633\text{-}2} \right)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 632} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {{- a} \times \sin \; \theta} \\{b \times \sin \; \theta} & {b \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (632)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (19A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 634} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (634)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 635]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (635)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 636]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (636)

Precoding method determiner 316 performs the calculations described in“(precoding method (19A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 637} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}} & (637)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 638} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {638\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {638\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (19A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 639} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (639)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (19A)” is not satisfied.

(Precoding Method (19B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 640} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (640)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 641} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (641)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 642} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (642)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 643]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×sin θ=0   (643-1)

−h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (643-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 644} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {644\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {644\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 645} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {645\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {645\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 646]

|a| ² +|b| ² =|u| ²   (646)

(|u|² is a parameter based on average transmiitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (19B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t). The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 647} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (647)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 648]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (648)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 649]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (649)

Precoding method determiner 316 performs the calculations described in“(precoding method (19B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 650} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {{- a} \times \sin \; \theta} \\{b \times \sin \; \theta} & {b \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (650)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 651} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {651\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {651\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (19B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 652} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (652)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 653]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (653)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 654]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (654)

Precoding method determiner 316 performs the calculations described in“(precoding method (19B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 655} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}} & (655)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 656} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {656\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {656\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (19B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 657} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \right.} \\{{\left. {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (657)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (19B)” is not satisfied.

(Precoding Method (20A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 658} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (658)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}} & (659)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 660} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{= {{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{= {\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} +}} \\{= {\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}\begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} - {{h_{22}(t)} \times}} \\{b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} - {{h_{22}(t)} \times}} \\{b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} + {{h_{22}(t)} \times}} \\{b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} + {{h_{22}(t)} \times}} \\{b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (660)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 661]

−h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (661-1)

h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (661-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 662} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {662\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {662\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 663} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {663\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {663\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 664]

|a| ² +|b| ² =|u| ²   (664)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (20A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 665} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (665)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 666]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (666)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 667]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ +e ^(jγ(t)) ×s ₂(t)   (667)

Precoding method determiner 316 performs the calculations described in“(precoding method (20A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 668} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {{- a} \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {b \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (668)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 669} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {669\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {669\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (20A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 670} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (670)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 671]

y ₁(t)=q ₁₁ ×s ₁(t)+q₁₂ ×e ^(jγ(t)) ×s ₂(t)   (671)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 672]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (672)

Precoding method determiner 316 performs the calculations described in“(precoding method (20A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 673} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} & (673)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 674} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {674\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {674\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (20A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 675} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{{K + 1}\;}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (675)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x 32 1, 2;y=1, 2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (20A)” is not satisfied.

(Precoding Method (20B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 676} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}} + \begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (676)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 677} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} + \begin{pmatrix}1 & 0 \\0 & e^{{j\; {\gamma {(t)}}}\;}\end{pmatrix} + \begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (677)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 678} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{{h_{22}(t)} \times \cos \; \delta}\;}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{{h_{22}(t)} \times \cos \; \delta}\;}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}} & (678)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 679]

h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (679-1)

−h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (679-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 680} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {680\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {680\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 681} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {681\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {681\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 682]

|a| ² +|b| ² =|u| ²   (682)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (20B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 683} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (683)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 684]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×3 ^(jγ(t)) ×s ₂(t)   (684)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 685]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (685)

Precoding method determiner 316 performs the calculations described in“(precoding method (20B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 686} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {{- a} \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {b \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (686)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 687} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {687\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {687\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (20B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 688} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (688)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 689]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (689)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 690]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (690)

Precoding method determiner 316 performs the calculations described in“(precoding method (20B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 691} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} & (691)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 692} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {692\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {692\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (20B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 693} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (693)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (20B)” is not satisfied.

(Precoding Method (21A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 694} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\; \cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (694)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 695} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (695)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 696} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{{e^{j\; \gamma}(t)}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (696)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 697]

−h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (697-1)

h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (697-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 698} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {698\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {698\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 699} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {699\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {699\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 700]

|a| ² +|b| ² =|u| ²   (700)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (21A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 701} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (701)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 702]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (702)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 703]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (703)

Precoding method determiner 316 performs the calculations described in“(precoding method (21A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 704} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {{- a} \times \cos \; \theta} \\{b \times \cos \; \theta} & {b \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (704)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 705} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {705\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {705\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (21A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 706} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (706)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 707]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (707)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 708]

y ₁(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (708)

Precoding method determiner 316 performs the calculations described in“(precoding method (21A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 709} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}} & (709)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 710} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {710\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {710\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (21A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 711} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (711)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (21A)” is not satisfied.

(Precoding Method (21B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 712} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (712)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 713} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (713)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 714} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}\; {s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (714)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 715]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (715-1)

−h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (715-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 716} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {716\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {716\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 717} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {717\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {717\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 718]

|a| ² +|b| ² +|u| ²   (718)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (21B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 719} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (719)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 720]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (720)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 721]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (721)

Precoding method determiner 316 performs the calculations described in“(precoding method (21B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 722} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {{- a} \times \cos \; \theta} \\{b \times \cos \; \theta} & {b \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (722)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 723} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {723\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {723\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (21B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 724} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (724)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 725]

y ₁(t)=q ₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (725)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 726]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (726)

Precoding method determiner 316 performs the calculations described in“(precoding method (21B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 727} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}} & (727)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 728} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {728\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {728\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (21B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 729} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (729)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (21B)” is not satisfied.

(Precoding Method (22A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 730} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (730)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 731} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (731)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 732} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}\; {s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (732)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 733]

−h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (733-1)

h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (733-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 734} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {734\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{integer}} \right)}}}} & \left( {734\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 735} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {735\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {735\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 736]

|a| ² |b| ² =|u| ²   (736)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (22A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 737} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (737)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 738]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (738)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 739]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (739)

Precoding method determiner 316 performs the calculations described in“(precoding method (22A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 740} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {{- a} \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {b \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (740)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 741} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {741\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{integer}} \right)}}}} & \left( {741\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (22A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 742} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (742)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 743]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (743)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 744]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (744)

Precoding method determiner 316 performs the calculations described in“(precoding method (22A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 745} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}} & (745)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 746} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {746\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{integer}} \right)}}}} & \left( {746\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (22A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 747} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (747)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (22A)” is not satisfied.

(Precoding Method (22B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 748} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (748)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 749} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (749)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 750} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (750)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 751]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (751-1)

−h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (751-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 752} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {752\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{integer}} \right)}}}} & \left( {752\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 753} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {753\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {753\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 754]

|a| ² +|b| ² =|u| ²   (754)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (22B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 755} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (755)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 756]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (756)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 757]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (757)

Precoding method determiner 316 performs the calculations described in“(precoding method (22B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}{\left\lbrack {{MATH}.\mspace{14mu} 758} \right\rbrack \mspace{14mu}} & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {{- a} \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {b \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (758)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 759} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {759\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {interger}} \right)}}}} & \left( {759\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (22B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 760} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (760)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 761]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (761)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 762]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (762)

Precoding method determiner 316 performs the calculations described in“(precoding method (22B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 763} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}} & (763)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 764} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {764\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {interger}} \right)}}}} & \left( {764\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (22B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 765} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (765)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (22B)” is not satisfied.

(Precoding Method (23A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 766} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (766)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 767} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \delta} & {\cos \; \delta} \\{\cos \; \delta} & {{- \sin}\; \delta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (767)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 768} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \delta} & {\cos \; \delta} \\{\cos \; \delta} & {{- \sin}\; \delta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{1}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (768)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 769]

h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (769-1)

h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (769-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 770} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {770\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {interger}} \right)}}}} & \left( {770\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 771} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {771\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {771\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 772]

|a| ² +|b| ² =|u| ²   (772)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (23A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 773} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (773)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 774]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (774)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 775]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (775)

Precoding method determiner 316 performs the calculations described in“(precoding method (23A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}{\left\lbrack {{MATH}.\mspace{14mu} 776} \right\rbrack \mspace{14mu}} & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {a \times \cos \; \theta} \\{b \times \cos \; \theta} & {{- b} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (776)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 777} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {777\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {interger}} \right)}}}} & \left( {777\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (23A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 778} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (778)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 779]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (779)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 780]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂ ×e ^(jγ(t)) ×s ₂(t)   (780)

Precoding method determiner 316 performs the calculations described in“(precoding method (23A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 781} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}} & (781)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 782} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {782\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {782\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (23A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{Math}.\mspace{14mu} 783} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (783)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (23A)” is not satisfied.

(Precoding Method (23B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{Math}.\mspace{14mu} 784} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {{\cos \; \delta}\;}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (784)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 785} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (785)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{Math}.\mspace{14mu} 786} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {{\cos \; \delta}\;}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (786)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 787]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (787-1)

h ₁₁(t)×a×sin δ×cos θ−h ₂₂(t)×b×cos δ×sin θ=0   (787-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 788} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {788\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {788\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 789} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {789\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {789\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 790]

|a| ² +|b| ² =|u| ²   (790)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (23B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 791} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (791)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 792]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (792)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 793]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (793)

Precoding method determiner 316 performs the calculations described in“(precoding method (23B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 794} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {a \times \cos \; \theta} \\{b \times \cos \; \theta} & {{- b} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (794)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 795} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {795\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {795\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (23B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 796} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (796)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 797]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (797)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 798]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (798)

Precoding method determiner 316 performs the calculations described in“(precoding method (23B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 799} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}} & (799)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 800} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {800\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n{\mspace{11mu} \;}{is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {800\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (23B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{Math}.\mspace{14mu} 801} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (801)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (23B)” is not satisfied.

(Precoding Method (24A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 802} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (802)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 803} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (803)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 804} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \; \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \; \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (804)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 805]

h ₁₁(t)×a×β×cos δ×cos θ+h ₂₂(t)×b×β×sin δ×sin θ=0   (805-1)

h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (805-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 806} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {806\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\text{}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {806\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 807} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {807\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {807\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 808]

|a| ² +|b| ² =|u| ²   (808)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (24A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 809} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (809)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 810]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (810)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 811]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (811)

Precoding method determiner 316 performs the calculations described in“(precoding method (24A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 812} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {a \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {{- b} \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (812)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 813} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {813\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {813\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (24A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 814} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (814)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 815]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (815)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 816]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (816)

Precoding method determiner 316 performs the calculations described in“(precoding method (24A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 817} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}} & (817)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 818} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {818\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {818\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (24A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 819} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (819)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (24A)” is not satisfied.

(Precoding Method (24B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 820} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (820)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 821} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (821)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 822} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \; \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \; \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (822)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 823]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (823-1)

h ₁₁(t)×a×β×sin δ×cos θ−h ₂₂(t)×b×β×cos δ×sin θ=0   (823-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 824} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {824\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {824\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 825} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {825\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {825\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 826]

|a| ² +|b| ² =|u| ²   (826)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (24B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 827} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (827)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 828]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (828)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 829]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (829)

Precoding method determiner 316 performs the calculations described in“(precoding method (24B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 830} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {a \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {{- b} \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (830)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 831} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {831\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {831\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (24B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 832} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (832)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 833]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (833)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 834]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (834)

Precoding method determiner 316 performs the calculations described in“(precoding method (24B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 835} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}} & (835)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 836} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {836\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {836\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (24B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 837} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (837)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (24B)” is not satisfied.

(Precoding Method (25A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 838} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (838)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 839} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j\; {({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (839)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 840} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j\; {({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times s} \\{{in}\; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; {({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; {({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; {({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; {({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (840)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 841]

h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×sin θ+h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×cos θ=0  (841-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×cos θ+h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0   (841-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 842} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {842\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {842\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 843} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {843\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {843\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 844]

|a| ² +|b| ² =|u| ²   (844)

(|u|² is a pararmeter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precolling Method (25A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 845} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (845)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 846]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (846)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 847]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (847)

Precoding method determiner 316 performs the calculations described in“(precoding method (25A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 848} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (848)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 849} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {849\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {849\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (25A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 850} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (850)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 851]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)×) s ₂(t)   (851)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 852]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (852)

Precoding method determiner 316 performs the calculations described in“(precoding method (25A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 853} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} & (853)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 854} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {854\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {854\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (25A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 855} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (855)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (25A)” is not satisfied.

(Precoding Method (25B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 856} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (856)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 857} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (857)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 858} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (858)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 859]

h ₁₁(t)×a×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×e ^(jω)×sin δ×sin θ=0   (859-1)

h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×sin θ−h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×cos θ=0  (859-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 860} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {860\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {860\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 861} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {861\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {861\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 862]

|a| ² +|b| ² =|u| ²   (862)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (25B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 863} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (863)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 864]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (864)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 865]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (865)

Precoding method determiner 316 performs the calculations described in“(precoding method (25B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 866} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (866)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 867} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {867\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {867\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (25B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 868} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (868)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 869]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (869)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 870]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (870)

Precoding method determiner 316 performs the calculations described in“(precoding method (25B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 871} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} & (871)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 872} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {872\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {872\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (25B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 873} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (873)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (25B)” is not satisfied.

(Precoding Method (26A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 874} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (874)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 875} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (875)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 876} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (876)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 877]

h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×sin θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×cosθ=0   (877-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×βe ^(jω)×cos δ×sin θ=0  (877-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 878} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {878\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {878\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 879} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {879\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {879\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 880]

|a| ² +|b| ² =|u| ²   (880)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (26A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 881} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (881)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 882]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (882)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 883]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (883)

Precoding method determiner 316 performs the calculations described in“(precoding method (26A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 884} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (884)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 885} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {885\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {885\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (26A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 886} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (886)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 887]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (887)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 888]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (888)

Precoding method determiner 316 performs the calculations described in“(precoding method (26A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 889} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (889)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 890} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {890\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {890\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (26A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 891} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (873)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (26A)” is not satisfied.

(Precoding Method (26B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 892} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (892)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 893} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (893)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 894} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (894)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 895]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×sin θ=0  (895-1)

h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×sin θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×cosθ=0   (895-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 896} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {896\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {896\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 897} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {897\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {897\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 898]

|a| ² +|b| ² =|u| ²   (898)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (26B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 899} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (899)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 900]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (900)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 901]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (901)

Precoding method determiner 316 performs the calculations described in“(precoding method (26B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 902} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (902)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 903} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {903\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {903\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (26B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 904} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (904)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 905]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (905)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 906]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (906)

Precoding method determiner 316 performs the calculations described in“(precoding method (26B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 907} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (907)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 908} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {908\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {908\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (26B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e,w(t) x s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 909} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (909)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (26B)” is not satisfied.

(Precoding Method (27A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 910} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (910)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 893} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (893)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 912} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (912)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 913]

−h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×sin θ−h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×cos θ=0  (913-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×cos θ−h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0   (913-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 914} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {914\text{-}1} \right) \\{\theta = {{- \delta} + {n\; {\pi_{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {914\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 915} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {915\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi_{radians}}}} & \left( {915\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 916]

|a| ² +|b| ² =|u| ²   (916)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (27A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 917} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (917)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 918]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (918)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 919]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (919)

Precoding method determiner 316 performs the calculations described in“(precoding method (27A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 920} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (920)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 921} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {921\text{-}1} \right) \\{\theta = {{- \delta} + {n\; {\pi_{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {921\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (27A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 922} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (922)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 923]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (923)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 924]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (924)

Precoding method determiner 316 performs the calculations described in“(precoding method (27A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 925} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (925)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 926} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {926\text{-}1} \right) \\{\theta = {{- \delta} + {n\; {\pi_{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {926\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (27A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 927} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (927)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (27A)” is not satisfied.

(Precoding Method (27B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 928} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{21}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (928)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 929} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}} & (929)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 930} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; \gamma}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (930)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 931]

h ₁₁(t)×a×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×e ^(jω)×sin δ×sin θ=0   (931-1)

−h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×sin θ+h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×cos θ=0  (931-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 932} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {932\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; {\pi_{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {932\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 933} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {933\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; {\pi_{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {933\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 934]

|a| ² +|b| ² =|u| ²   (934)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (27B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 935} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (935)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 936]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (936)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 937]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (937)

Precoding method determiner 316 performs the calculations described in“(precoding method (27B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 938} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \mspace{14mu} \theta} \\{e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{b \times e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {b \times e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (938)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 939} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {939\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {939\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (27B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 940} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (940)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 941]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (941)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 942]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (942)

Precoding method determiner 316 performs the calculations described in“(precoding method (27B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 943} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \mspace{14mu} \theta} \\{e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}} & (943)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 944} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {944\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {944\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (27B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 945} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (945)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (27B)” is not satisfied.

(Precoding Method (28A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 946} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (946)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 947} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{\beta \times e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (947)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

     [MATH.  948]                                           (948)$\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j\; {({\mu \; + \; \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j\; {({\omega \; + \; \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\mu} \times} \\{{\cos \; \delta \times \cos \; \theta} - {{h_{22}(t)} \times b \times}} \\{\beta \times e^{j\omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu \; + \; \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} - {{h_{22}(t)} \times b \times \beta \times}} \\{e^{j{({\omega \; + \; \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\mu} \times} \\{{\sin \; \delta \times \cos \; \theta} + {{h_{22}(t)} \times b \times}} \\{\beta \times e^{j\omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu \; + \; \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} + {{h_{22}(t)} \times b \times \beta \times}} \\{e^{j{({\omega \; + \; \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{s_{1}(t)} \\\begin{matrix}e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{matrix}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 949]

−h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×sin θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×cosθ=0   (949-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×cos θ−h ₂₂(t)×b×β×e ^(jω)×cos δ×sin θ=0  (949-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 950} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {950\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {950\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 951} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {951\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {951\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 952]

|a| ² +|b| ² =|u| ²   (952)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (28A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 953} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (953)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 954]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (954)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 955]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (955)

Precoding method determiner 316 performs the calculations described in“(precoding method (28A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 956} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{\beta \times e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (956)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 957} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {957\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {957\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (28A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 958} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (958)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 959]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (959)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 960]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (960)

Precoding method determiner 316 performs the calculations described in“(precoding method (28A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 961} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (961)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 962} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {962\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {962\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (28A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 963} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (963)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (28A)” is not satisfied.

(Precoding Method (28B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 964} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (964)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 965} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (965)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 966} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (966)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 967]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×sin θ=0  (967-1)

−h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×sin θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×cosθ=0   (967-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 968} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {968\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {968\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 969} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {969\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {969\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 970]

|a| ² +|b| ² =|u| ²   (970)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (28B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 971} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (971)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 972]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (972)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 973]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (973)

Precoding method determiner 316 performs the calculations described in“(precoding method (28B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 974} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (974)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 975} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {975\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {975\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (28B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 976} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (976)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 977]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (977)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 978]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (978)

Precoding method determiner 316 performs the calculations described in“(precoding method (28B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 979} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (979)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 980} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {980\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {980\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (28B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 981} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (981)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (28B)” is not satisfied.

(Precoding Method (29A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 982} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (982)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 983} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (983)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 984} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{{e^{j\; \gamma}(t)}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (984)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 985]

−h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×sin θ=0  (985-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×e ^(jω)×cos δ×cos θ=0   (985-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 986} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {986\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {986\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 987} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {987\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {987\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 988]

|a| ² +|b| ² =|u| ²   (988)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (29A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 989} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (989)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 990]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (990)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 991]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (991)

Precoding method determiner 316 performs the calculations described in“(precoding method (29A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 992} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (992)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 993} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {993\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {993\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (29A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 994} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (994)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 995]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (995)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 996]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (996)

Precoding method determiner 316 performs the calculations described in“(precoding method (29A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 997} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (997)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 998} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {998\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {998\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (29A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 999} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (999)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (29A)” is not satisfied.

(Precoding Method (29B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1000} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1000)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1001} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1001)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1002} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{{e^{j\; \gamma}(t)}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1002)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1003]

h ₁₁(t)×a×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (1003-1)

−h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ+h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (1003-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1004} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1004\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {interger}} \right)}}}} & \left( {1004\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1005} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1005\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1005\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1006]

|a| ² +|b| ² =|u| ²   (1006)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (29B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1007} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1007)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1008]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1008)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1009]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1009)

Precoding method determiner 316 performs the calculations described in“(precoding method (29B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1010} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1010)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1011} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1011\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {interger}} \right)}}}} & \left( {1011\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (29B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1012} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1012)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1013]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1013)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1014]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1014)

Precoding method determiner 316 performs the calculations described in“(precoding method (29B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1015} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1015)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1016} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1016\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {interger}} \right)}}}} & \left( {1016\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (29B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1017} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1017)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (29B)” is not satisfied.

(Precoding Method (30A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1018} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1018)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{85mu} \left\lbrack {{MATH}.\mspace{14mu} 1019} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1019)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1020} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu}\cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega \times \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu}\sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega \times \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1020)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1021]

−h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×sinθ=0   (1021-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×cos δ×cos θ=0  (1021-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1022} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1022\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {interger}} \right)}}}} & \left( {1022\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1023} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1023\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1023\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1024]

|a| ² +|b| ² =|u| ²   (1024)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (30A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1025} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1025)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1026]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1026)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1027]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1027)

Precoding method determiner 316 performs the calculations described in“(precoding method (30A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1028} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{a \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1028)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1029} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1029\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1029\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (30A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1030} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1030)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1031]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1031)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1032]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1032)

Precoding method determiner 316 performs the calculations described in“(precoding method (30A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1033} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1033)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1034} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1034\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1034\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (30A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{ \left\lbrack {{MATH}.\mspace{14mu} 1035} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1035)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (30A)” is not satisfied.

(Precoding Method (30B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1036} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1036)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1037} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1037)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1038} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times s\; {in}\; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1038)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1039]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×cos θ=0  (1039-1)

−h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×sinθ=0   (1039-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1040} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1040\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1040\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1041} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1041\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1041\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1042]

|a| ² +|b| ² =|u| ²   (1042)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (30B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1043} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1043)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1044]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1044)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1045]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1045)

Precoding method determiner 316 performs the calculations described in“(precoding method (30B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1046} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{a \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1046)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1047} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1047\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1047\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (30B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1048} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1048)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1049]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1049)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1050]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1050)

Precoding method determiner 316 performs the calculations described in“(precoding method (30B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1051} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1051)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1052} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1052\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1052\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (30B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1053} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1053)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (30B)” is not satisfied.

(Precoding Method (31A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1054} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1054)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{85mu} \left\lbrack {{MATH}.\mspace{14mu} 1055} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1055)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1056} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1056)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1057]

h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×cos θ+h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×sin θ=0  (1057-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×e ^(jω)×cos δ×cos θ=0   (1057-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1058} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1058\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1058\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1059} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1059\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1059\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1060]

|a| ² +|b| ² =|u| ²   (1060)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (31A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1061} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1061)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1062]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1062)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1063]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1063)

Precoding method determiner 316 performs the calculations described in“(precoding method (31A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1064} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1064)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1065} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1065\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1065\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (31A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1066} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1066)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1067]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1067)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1068]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1068)

Precoding method determiner 316 performs the calculations described in“(precoding method (31A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1069} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1069)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1070} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1070\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1070\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (31A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1071} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1071)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (31A)” is not satisfied.

(Precoding Method (31B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1072} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1072)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1073} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1073)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1074} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times e^{j\; {({\omega \times \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times e^{j\; \mu} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times e^{j\; {({\mu \times \lambda})}} \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times e^{j\; {({\omega \times \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1074)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1075]

h ₁₁(t)×a×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (1075-1)

h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (1075-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1076} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1076\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1076\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1077} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1077\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1077\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1078]

|a| ² +|b| ² =|u| ²   (1078)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (31B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1079} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1079)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1080]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1080)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1081]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1081)

Precoding method determiner 316 performs the calculations described in“(precoding method (31B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1082} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1082)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1083} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1083\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1083\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (31B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1084} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1084)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1085]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1085)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1086]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1086)

Precoding method determiner 316 performs the calculations described in“(precoding method (31B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1087} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} & (1087)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1088} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1088\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1088\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (31B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1089} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1089)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (31B)” is not satisfied.

(Precoding Method (32A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1090} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1090)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, n, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1091} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1091)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1092} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega \times \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu \times \lambda})}} \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega \times \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1092)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1093]

h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×cos θ+h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×sinθ=0   (1093-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×β×e ^(jω)×cos δ×cos θ=0  (1093-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1094} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1094\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1094\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1095} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {1095\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1095\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1096]

|a| ² +|b| ² =|u| ²   (1096)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (32A-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1097} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1097)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1098]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1098)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1099]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1099)

Precoding method determiner 316 performs the calculations described in“(precoding method (32A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1100} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1100)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1101} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {1101\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1101\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (32A-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1102} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1102)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1103]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1103)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1104]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1104)

Precoding method determiner 316 performs the calculations described in“(precoding method (32A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1105} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1105)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1106} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {1106\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1106\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (32A))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1107} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1107)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (32A)” is not satisfied.

(Precoding Method (32B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1108} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1108)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1109} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1109)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1110} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{s_{1}(t)} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1110)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1111]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×cos θ=0  (1111-1)

h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×sinθ=0   (1111-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1112} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {1112\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1112\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1113} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {1113\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1113\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1114]

|a| ² +|b| ² =|u| ²   (1114)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₂(t), a phase-change isimplemented, but the configuration “mapped baseband signal s₁(t) is notaffected (interference) by mapped baseband signal s₂(t) and mappedbaseband signal s₂(t) is not affected (interference) by mapped basebandsignal s₁(t)” is maintained.

(Precoding Method (32B-1))

FIG. 10 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B andprecoding method determiner 316 illustrated in FIG. 10 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1115} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1115)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1116]

z ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1116)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1117]

z ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1117)

Precoding method determiner 316 performs the calculations described in“(precoding method (32B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1118} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1118)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1119} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1119\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1119\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (32B-2))

FIG. 11 illustrates a configuration of a communications stationdifferent from FIG. 10. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 11 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1120} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1120)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1121]

y ₁(t)=q ₁₁ ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1121)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1122]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1122)

Precoding method determiner 316 performs the calculations described in“(precoding method (32B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1123} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1123)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1124} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1124\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1124\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 11 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 11 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (32B))

Phase changer 1001B illustrated in FIG. 10 and FIG. 11 receives an inputof mapped signal s₂(t) output from mapper 304B, applies a phase-change,and outputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1125} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1125)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001B is not provided in FIG. 10 and FIG. 11—in thereception device, it is likely that r₁(t) and r₂(t) are in a continuous(small amount of fluctuation) reception state. Accordingly, regardlessof the reception field intensity being high, there is a possibility ofbeing continuously in a state in which signal demultiplexing isdifficult.

On the other hand, in FIG. 10 and FIG. 11, when phase changer 1001B ispresent, in the reception device, since r₁(t) and r₂(t) are implementedwith a time (or frequency) phase-change by the transmission device, theycan be kept from being in continuous reception state. Accordingly, it islikely that continuously being in a state in which signal demultiplexingis difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 10and FIG. 11, when the phase changer is arranged after the weightingsynthesizer, “precoding method (32B)” is not satisfied.

(Communications Station Configuration (4))

Communications station configurations different from the configurationsillustrated in FIG. 10 and FIG. 11 are illustrated in FIG. 12 and FIG.13. Operations that are the same as in FIG. 10 and FIG. 11 share likereference marks. The configurations illustrated in FIG. 12 and FIG. 13differ from the configurations illustrated in FIG. 10 and FIG. 11 inthat phase changer 1001A is added.

Phase changer 1001A receives inputs of mapped signal 305B andtransmission method/frame configuration signal 319, changes the phase ofmapped signal 305B based on transmission method/frame configurationsignal 319, and outputs phase-changed signal 1002B.

Note that in FIG. 12 and FIG. 13, weighting synthesizer 306A performsprocessing on phase-changed signal 1002A as an input instead of mappedsignal 305A.

(Precoding Method (33A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1126} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1126)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1127} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1127)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1128} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}{e^{j\; ɛ}(t)} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{{e^{j\; ɛ}(t)}{s_{1}(t)}} \\{{e^{j\; \gamma}(t)}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1128)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1129]

h ₁₁(t)×a×cos δ×sin θ+h ₂₂(t)×b×sin δ×cos θ=0   (1129-1)

h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (1129-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1130} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1130\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1130\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1131} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1131\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1131\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1132]

|a| ² +|b| ² =|u| ²   (1132)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (33A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1133} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1133)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1134]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1134)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1135]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1135)

Precoding method determiner 316 performs the calculations described in“(precoding method (33A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1136} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {a \times \sin \; \theta} \\{b \times \sin \; \theta} & {{- b} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1136)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1137} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1137\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1137\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (33A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1138} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1138)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1139]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1139)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1140]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1140)

Precoding method determiner 316 performs the calculations described in“(precoding method (33A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1141} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}} & (1141)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1142} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1142\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1142\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (33A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1143} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1143)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (33A)” is not satisfied.

(Precoding Method (33B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1144} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1144)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1145} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1145)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1146} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {\mu {(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {\mu {(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1146)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1147]

h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×cos θ=0   (1147-1)

h ₁₁(t)×a×sin δ×sin θ−h ₂₂(t)×b×cos δ×cos θ=0   (1147-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1148} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1148\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1148\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1149} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1149\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1149\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1150]

|a| ² +|b| ² =|u| ²   (1150)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (33B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1151} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1151)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1152]

z ₁(t)=q ₁₁ e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1152)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1153]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1153)

Precoding method determiner 316 performs the calculations described in“(precoding method (33B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1154} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \; \theta} & {a \times \sin \; \theta} \\{b \times \sin \; \theta} & {{- b} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1154)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1155} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1155\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1155\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (33B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1156} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1156)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1157]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1157)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1158]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1158)

Precoding method determiner 316 performs the calculations described in“(precoding method (33B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1159} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}} & (1159)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1160} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1160\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1160\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (33B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1161} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1161)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (33B)” is not satisfied.

(Precoding Method (34A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1162} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {{\cos \; \delta}\;}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1162)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 1163} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}a & 0 \\0 & {b\;}\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & {e^{j\; {\gamma {(t)}}}\;}\end{pmatrix}} + \begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1163)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 1164} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}} & (1164)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1165]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (1165-1)

h ₁₁(t)×a×β×sin δ×cos θ−h ₂₂(t)×b×β×cos δ×sin θ=0   (1165-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1166} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1166\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1166\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1167} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1167\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1167\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1168]

|a| ² +|b| ² =|u| ²   (1168)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (34A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1169} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1169)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1170]

z ₁(t)=q ₁₁ e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1170)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1171]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) s ₁(t)+q ₂₂ 33 e ^(jγ(t)) ×s ₂(t)   (1171)

Precoding method determiner 316 performs the calculations described in“(precoding method (34A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1172} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {a \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {{- b} \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1172)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1173} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1173\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1173\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (34A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1174} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1174)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1175]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1175)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1176]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1176)

Precoding method determiner 316 performs the calculations described in“(precoding method (34A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1177} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}} & (1177)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1178} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1178\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1178\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (34A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 1178} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1179)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (34A)” is not satisfied.

(Precoding Method (34B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1180} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1180)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 1181} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}} + \begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1181)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{20mu} \left\lbrack {{MATH}.\mspace{14mu} 1182} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}} & (1182)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1183]

h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (1183-1)

h ₁₁(t)×a×β×sin δ×sin θ−h ₂₂(t)×b×β×cos δ×cos θ=0   (1183-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1184} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1184\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1184\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1185} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1185\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1185\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1186]

|a| ² +|b| ² =|u| ²   (1186)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (34B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1187} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1187)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1188]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1188)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1189]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1189)

Precoding method determiner 316 performs the calculations described in“(precoding method (34B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1190} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \mspace{14mu} \theta} & {a \times \beta \times \sin \mspace{14mu} \theta} \\{b \times \beta \times \sin \mspace{14mu} \theta} & {{- b} \times \beta \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1190)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1191} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1191\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1191\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (34B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1192} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1192)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1193]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1193)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1194]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1194)

Precoding method determiner 316 performs the calculations described in“(precoding method (34B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1195} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta}\end{pmatrix}} & (1195)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1196} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1196\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1196\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (34B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1197} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1197)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (34B)” is not satisfied.

(Precoding Method (35A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1198} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1198)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1199} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1199)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

     [MATH.  1200] (1200) $\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1201]

−h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (1201-1)

h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (1201-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1202} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1202\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1202\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1203} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1203\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1203\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1204]

|a| ² +|b| ² =|u| ²   (1204)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (35A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1205} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1205)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1206]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1206)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1207]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1207)

Precoding method determiner 316 performs the calculations described in“(precoding method (35A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1208} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \mspace{14mu} \theta} & {{- a} \times \sin \mspace{14mu} \theta} \\{b \times \sin \mspace{14mu} \theta} & {b \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1208)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1209} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1209\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1209\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (35A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1210} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1210)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1211]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1211)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1212]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1212)

Precoding method determiner 316 performs the calculations described in“(precoding method (35A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1213} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{pmatrix}} & (1213)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1214} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1214\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1214\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (35A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1215} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1215)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (35A)” is not satisfied.

(Precoding Method (35B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1216} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1216)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1217} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1217)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following relation equation holds true.

     [MATH.  1218] (1218) $\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1219]

h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (1219-1)

−h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (1219-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1220} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1220\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1220\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1221} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1221\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1221\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1222]

|a| ² +|b| ² =|u| ²   (1222)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (35B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1223} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1223)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1224]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)×s) ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1224)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1225]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1225)

Precoding method determiner 316 performs the calculations described in“(precoding method (35B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1226} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \cos \mspace{14mu} \theta} & {{- a} \times \sin \mspace{14mu} \theta} \\{b \times \sin \mspace{14mu} \theta} & {b \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1226)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1227} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1227\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1227\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (35B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t). Coefficient multiplied signal 402B output by coefficientmultiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1228} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1228)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1229]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1229)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1230]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1230)

Precoding method determiner 316 performs the calculations described in“(precoding method (35B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1231} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{pmatrix}} & (1231)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1232} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1232\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1232\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (35B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e)^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1233} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1233)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andhx_(y, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (35B)” is not satisfied.

(Precoding Method (36A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1234} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1234)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1235} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {{- \beta} \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {\beta \times \cos \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1235)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

     [MATH.  1236] (1236) $\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1237]

−h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (1237-1)

h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (1237-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1238} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1238\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1238\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1239} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1239\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1239\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1240]

|a| ² +|b| ² =|u| ²   (1240)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (36A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1241} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1241)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1242]

z ₁(t)=q ₁₁ ××e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1242)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1243]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1243)

Precoding method determiner 316 performs the calculations described in“(precoding method (36A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1244} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {{- \beta} \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {\beta \times \cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \mspace{14mu} \theta} & {{- a} \times \beta \times \sin \mspace{14mu} \theta} \\{b \times \beta \times \sin \mspace{14mu} \theta} & {b \times \beta \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1244)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1245} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1245\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1245\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (36A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1246} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1246)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1247]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1247)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1248]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1248)

Precoding method determiner 316 performs the calculations described in“(precoding method (36A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1249} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \mspace{14mu} \theta} & {{- \beta} \times \sin \mspace{14mu} \theta} \\{\beta \times \sin \mspace{14mu} \theta} & {\beta \times \cos \mspace{14mu} \theta}\end{pmatrix}} & (1249)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1250} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1250\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1250\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (36A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e)^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1251} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1251)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (36A)” is not satisfied.

(Precoding Method (36B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1252} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1252)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1253} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1253)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1254} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \; \cos \; \theta} -}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \; \cos \; \theta} +}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1254)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1255]

h ₁₁(t)×a×β×cos δ×cos θ−h₂₂(t)×b×β×sin δ×sin θ=0   (1255-1)

−h ₁₁(t)×a×β×sin δ×sin θ+h₂₂(t)×b×β×cos δ×cos θ=0   (1255-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1256} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1256\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1256\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1257} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1257\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1257\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1258]

|a| ² +|b| ² =|u| ²   (1258)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (36B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1259} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1259)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1260]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1260)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1261]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1261)

Precoding method determiner 316 performs the calculations described in“(precoding method (36B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1262} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \cos \; \theta} & {{- a} \times \beta \times \sin \; \theta} \\{b \times \beta \times \sin \; \theta} & {b \times \beta \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1262)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1263} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1263\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1263\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (36B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1264} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1264)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1265]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1265)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1266]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1266)

Precoding method determiner 316 performs the calculations described in“(precoding method (36B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1267} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta} \\{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta}\end{pmatrix}} & (1267)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1268} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1268\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1268\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)).

Similarly, based on the values of q₂₁ and q₂₂, weighting synthesizer306B performs weighting synthesis calculations, and outputs weightedsignal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (36B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e)^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1269} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1269)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (36B)” is not satisfied.

(Precoding Method (37A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1270} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1270)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1271} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1271)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and y(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1272} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \; \sin \; \theta} -} & {{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta} \\{{{h_{11}(t)} \times a \times \sin \; \delta \times \; \sin \; \theta} +} & {{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta} & {{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1272)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1273]

−h ₁₁(t)×a×cos δ×cos θ−h ₂₂(t)×b×sin δ×sin θ=0   (1273-1)

h ₁₁(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (1273-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1274} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1274\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1274\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1275} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1275\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1275\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1276]

|a| ² +|b| ² =|u| ²   (1276)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (37A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1277} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1277)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1278]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1278)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1279]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1279)

Precoding method determiner 316 performs the calculations described in“(precoding method (37A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1280} \right) & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {{- a} \times \cos \; \theta} \\{b \times \cos \; \theta} & {b \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1280)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1281} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1281\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1281\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (37A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1282} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1282)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1283]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1283)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1284]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1284)

Precoding method determiner 316 performs the calculations described in“(precoding method (37A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1285} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}} & (1285)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1286} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1286\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1286\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (37A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e)^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1287} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1287)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (37A)” is not satisfied.

(Precoding Method (37B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1288} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1288)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1289} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1289)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1290} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1290)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1291]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (1291-1)

−h ₁₁(t)×a×sin δ×cos θ+h ₂₂(t)×b×cos δ×sin θ=0   (1291-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1292} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1292\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}\mspace{14mu} {integer}} \right)}}}} & \left( {1292\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1293} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1293\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1293\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1294]

|a| ² +|b| ² =|u| ²   (1294)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precolling Method (37B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1295} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1295)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1296]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1296)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1297]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1297)

Precoding method determiner 316 performs the calculations described in“(precoding method (37B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1298} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {{- a} \times \cos \; \theta} \\{b \times \cos \; \theta} & {b \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1298)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1299} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1299\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1299\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (37B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1300} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1300)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1301]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ e ^(jγ(t)) ×s ₂(t)   (1301)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1302]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1302)

Precoding method determiner 316 performs the calculations described in“(precoding method (37B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1303} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {{- \cos}\; \theta} \\{\cos \; \theta} & {\sin \; \theta}\end{pmatrix}} & (1303)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1304} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1304\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1304\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (37B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e)^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1305} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1305)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (37B)” is not satisfied.

(Precoding Method (38A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1306} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1306)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1307} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & \left( 1307 \right.\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1308} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}}} \\{{{\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times s\; {in}\; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1308)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1309]

−h ₁₁(t)×a×β×cos δ×cos θ−h ₂₂(t)×b×β×sin δ×sin θ=0   (1309-1)

h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (1309-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1310} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1310\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1310\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1311} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1311\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1311\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1312]

|a| ² +|b| ² =|u| ²   (1312)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (38A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1313} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1313)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1314]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1314)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1315]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1315)

Precoding method determiner 316 performs the calculations described in“(precoding method (38A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1316} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {{- a} \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {b \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1316)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1317} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1317\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1317\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (38A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1318} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1318)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1319]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1319)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1320]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1320)

Precoding method determiner 316 performs the calculations described in“(precoding method (38A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1321} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta} \\{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta}\end{pmatrix}} & (1321)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1322} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1322\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1322\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (38A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e)^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1323} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1323)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (38A)” is not satisfied.

(Precoding Method (38B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1324} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\; \cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\; \sin \mspace{14mu} \delta} \\{{h_{11}(t)}\; \sin \mspace{14mu} \delta} & {{h_{22}(t)}\; \cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1324)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1325} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta} \\{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1325)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

     [MATH.  1326] (1326) $\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {{- \beta} \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {\beta \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1327]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (1327-1)

−h ₁₁(t)×a×β×sin δ×cos θ+h ₂₂(t)×b×β×cos δ×sin θ=0   (1327-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1328} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1328\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1328\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1329} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1329\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1329\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1330]

|a| ² +|b| ² =|u| ²   (1330)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (38B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1331} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1331)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1332]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1332)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1333]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₂(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1333)

Precoding method determiner 316 performs the calculations described in“(precoding method (38B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1334} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta} \\{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \mspace{14mu} \theta} & {{- a} \times \beta \times \cos \mspace{14mu} \theta} \\{b \times \beta \times \cos \mspace{14mu} \theta} & {b \times \beta \times \sin \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1334)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1335} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1335\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1335\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (38B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1336} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1336)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1337]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1337)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1338]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1338)

Precoding method determiner 316 performs the calculations described in“(precoding method (38B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1339} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \mspace{14mu} \theta} & {{- \beta} \times \cos \mspace{14mu} \theta} \\{\beta \times \cos \mspace{14mu} \theta} & {\beta \times \sin \mspace{14mu} \theta}\end{pmatrix}} & (1339)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1340} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1340\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1340\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)).

Similarly, based on the values of q₂₁ and q₂₂, weighting synthesizer306B performs weighting synthesis calculations, and outputs weightedsignal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (38B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1341} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; d}(t)} & {h_{12,\; d}(t)} \\{h_{21,\; d}(t)} & {h_{22,\; d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K\; + \; 1}}\begin{pmatrix}{h_{11,\; s}(t)} & {h_{12,\; s}(t)} \\{h_{21,\; s}(t)} & {h_{22,\; s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1341)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (38B)” is not satisfied.

(Precoding Method (39A)) In a state such as in FIG. 2, signals r₁(t),r₂(t) that are received by a reception device can be applied as follows(note that δ is greater than or equal to 0 radians and less than 2πradians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1342} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1342)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1343} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1343)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1344} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1344)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1345]

h ₁₁(t)×a×cos δ×cos θ+h ₂₂(t)×b×sin δ×sin θ=0   (1345-1)

h ₁₂(t)×a×sin δ×sin θ+h ₂₂(t)×b×cos δ×cos θ=0   (1345-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1346} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1346\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1346\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1347} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1347\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1347\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1348]

|a| ² +|b| ² =|u| ²   (1348)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (39A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1349} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1349)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1350]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1350)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1351]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1351)

Precoding method determiner 316 performs the calculations described in“(precoding method (39A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1352} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \; \theta} & {a \times \cos \; \theta} \\{b \times \cos \; \theta} & {{- b} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1352)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1353} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1353\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1353\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (39A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1354} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1354)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1355]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1355)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1356]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) s ₂(t)   (1356)

Precoding method determiner 316 performs the calculations described in“(precoding method (39A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1357} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}} & (1357)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1358} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}}{and}} & \left( {1358\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1358\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (39A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1359} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1359)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (39A)” is not satisfied.

(Precoding Method (39B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1360} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1360)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1361} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1361)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1362} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \; \theta} & {\cos \; \theta} \\{\cos \; \theta} & {{- \sin}\; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1362)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1363]

h ₁₁(t)×a×cos δ×sin θ−h ₂₂(t)×b×sin δ×cos θ=0   (1363-1)

h ₁₁(t)×a×sin δ×cos θ−h ₂₂(t)×b×cos δ×sin θ=0   (1363-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1364} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1364\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1364\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1365} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1365\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1365\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1366]

|a| ² +|b| ² =|u| ²   (1366)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (39B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1367} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1367)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1368]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1368)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1369]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1369)

Precoding method determiner 316 performs the calculations described in“(precoding method (39B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1370} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta} \\{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \sin \mspace{14mu} \theta} & {a \times \cos \mspace{14mu} \theta} \\{b \times \cos \mspace{14mu} \theta} & {{- b} \times \sin \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1370)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated.

Here, based on feedback information from a terminal, precoding methoddeterminer 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1371} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1371\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1371\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (39B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1372} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1372)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1373]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1373)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1374]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1374)

Precoding method determiner 316 performs the calculations described in“(precoding method (39B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1375} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta} \\{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta}\end{pmatrix}} & (1375)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1376} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1376\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1376\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (39B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1377} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1377)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (39B)” is not satisfied.

(Precoding Method (40A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1378} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\sin \mspace{14mu} \delta} \\{{h_{11}(t)}\sin \mspace{14mu} \delta} & {{h_{22}(t)}\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1378)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1379} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \mspace{14mu} \theta} & {\beta \times \cos \mspace{14mu} \theta} \\{\beta \times \cos \mspace{14mu} \theta} & {{- \beta} \times \sin \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1379)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

     [MATH.  1380] (1380) $\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1381]

h ₁₁(t)×a×β×cos δ×cos θ+h ₂₂(t)×b×β×sin δ×sin θ=0   (1381-1)

h ₁₁(t)×a×β×sin δ×sin θ+h ₂₂(t)×b×β×cos δ×cos θ=0   (1381-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1382} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1382\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1382\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1383} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1383\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1383\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1384]

|a| ² +|b| ² =|u| ²   (1078)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precolling Method (40A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1385} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1385)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1386]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1386)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1387]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1387)

Precoding method determiner 316 performs the calculations described in“(precoding method (40A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1388} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {a \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {b \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1388)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1389} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1389\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1389\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (40A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1390} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1390)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1391]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1391)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1392]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₁(t)   (1392)

Precoding method determiner 316 performs the calculations described in“(precoding method (40A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1393} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}} & (1393)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1394} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1394\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1394\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (40A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{85mu} {\left\lbrack {{MATH}.\mspace{14mu} 1395} \right\rbrack \mspace{695mu} (1395)}} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & \;\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (40A)” is not satisfied.

(Precoding Method (40B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1396} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1396)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1397} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1397)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1398} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}}} \\{{\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{\sin \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1398)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1399]

h ₁₁(t)×a×β×cos δ×sin θ−h ₂₂(t)×b×β×sin δ×cos θ=0   (1399-1)

h ₁₁(t)×a×β×sin δ×cos θ−h ₂₂(t)×b×βcos δ×sin θ=0   (1399-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1400} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1400\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1400\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1401} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1401\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1401\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1402]

|a| ² +|b| ² =|u| ²   (1402)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (40B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1403} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1403)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1404]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1404)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1405]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1405)

Precoding method determiner 316 performs the calculations described in“(precoding method (40B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1405} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times \sin \; \theta} & {\beta \times \cos \; \theta} \\{\beta \times \cos \; \theta} & {{- \beta} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times \sin \; \theta} & {a \times \beta \times \cos \; \theta} \\{b \times \beta \times \cos \; \theta} & {{- b} \times \beta \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1406)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1407} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a}} & \left( {1407\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1407\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (40B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1408} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1408)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1409]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1409)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1410]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1410)

Precoding method determiner 316 performs the calculations described in“(precoding method (40B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1411} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times \sin \mspace{14mu} \theta} & {\beta \times \cos \mspace{14mu} \theta} \\{\beta \times \cos \mspace{14mu} \theta} & {{- \beta} \times \sin \mspace{14mu} \theta}\end{pmatrix}} & (1411)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1412} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}}} & \left( {1412\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1412\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (40B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1413} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1413)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andhx_(y, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (40B)” is not satisfied.

(Precoding Method (41A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1414} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \mspace{14mu} \delta} & {{- \sin}\mspace{14mu} \delta} \\{\sin \mspace{14mu} \delta} & {\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \mspace{14mu} \delta} & {{- {h_{22}(t)}}\sin \mspace{14mu} \delta} \\{{h_{11}(t)}\sin \mspace{14mu} \delta} & {{h_{22}(t)}\cos \mspace{14mu} \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1414)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1415} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \mspace{14mu} \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1415)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

     [MATH.  1416] (1416) $\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j\; {({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( \begin{matrix}\begin{matrix}{{{h_{11}(t)} \times a \times e^{j\mu} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times e^{j\omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times e^{j\mu} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times e^{j\omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \right)\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}}}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1417]

h ₁₁(t)×a×e ^(jμ+λ))×cos δ×sin θ+h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×cos θ=0  (1417-1)

h ₁₁(t)×a×e ^(j(μ))×sin δ×cos θ+h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0  (1417-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1418} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1418\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1418\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1419} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1419\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1419\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1420]

|a| ² +|b| ² =|u| ²   (1420)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₁(t) and mapped basebandsignal s₂(t), phase-change is implemented, but the configuration “mappedbaseband signal s₁(t) is not affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) is not affected(interference) by mapped baseband signal s₁(t)” is maintained.

(Precoding Method (41A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1421} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1421)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1422]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1422)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1423]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1423)

Precoding method determiner 316 performs the calculations described in“(precoding method (41A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1424} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \mspace{14mu} \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \mspace{11mu} \theta} & {a \times e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{b \times e^{j\; \omega} \times \sin \mspace{11mu} \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \cos \mspace{14mu} \theta}\end{pmatrix}}\end{matrix} & (1424)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1425} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1425\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1425\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (41A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1426} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1426)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1427]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1427)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1428]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1428)

Precoding method determiner 316 performs the calculations described in“(precoding method (41A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1429} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \mspace{14mu} \theta} & {e^{j{({\mu + \lambda})}} \times \sin \mspace{14mu} \theta} \\{e^{j\; \omega} \times \sin \mspace{14mu} \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \mspace{14mu} \theta}\end{pmatrix}} & (1429)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1430} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1430\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1430\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)).

Similarly, based on the values of q₂₁ and q₂₂, weighting synthesizer306B performs weighting synthesis calculations, and outputs weightedsignal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (41A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1431} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1431)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (41A)” is not satisfied.

(Precoding Method (41B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1432} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1432)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1433} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1433)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1434} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\;}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; {({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; {({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times} \\{e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; {({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; {({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1434)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1435]

h ₁₁(t)×a×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (1435-1)

h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (1435-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1436} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1436\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{interger}} \right)}}}} & \left( {1436\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1437} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1437\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1437\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1438]

|a| ² +|b| ² =|u| ²   (1438)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (41B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1439} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1439)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1440]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1440)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1441]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1441)

Precoding method determiner 316 performs the calculations described in“(precoding method (41B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1442} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1442)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1443} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1443\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{interger}} \right)}}}} & \left( {1443\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (41B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1444} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1444)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1445]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1445)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1446]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1446)

Precoding method determiner 316 performs the calculations described in“(precoding method (41B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1447} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \cos \; \theta}\end{pmatrix}} & (1447)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1448} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1448\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}{\mspace{11mu} \;}{an}{\mspace{11mu} \;}{interger}} \right)}}}} & \left( {1448\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (41B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1449} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1449)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andhx_(y, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (41B)” is not satisfied.

(Precoding Method (42A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1450} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1450)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{76mu} \left\lbrack {{MATH}.\mspace{14mu} 1451} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1451)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1452} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\;}\end{pmatrix}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; {({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; \mu} \times \sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; {({\mu + \lambda})}} \times \sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; {({\omega + \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1452)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1453]

h ₁₁(t)×a××β×e ^(j(μ+λ))×cos δ×sin θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×cosθ=0   (1453-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×cos θ+h ₂₂(t)×b×β×e ^(jω)×cos δ×sin θ=0  (1453-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1454} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1454\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1454\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1455} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1455\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1455\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1456]

|a| ² +|b| ² =|u| ²   (1456)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (42A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1457} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1457)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1458]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1458)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1459]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1459)

Precoding method determiner 316 performs the calculations described in“(precoding method (42A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1460} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {a \times \beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times \beta \times e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1460)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1461} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1461\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1461\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (42A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1462} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1462)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1463]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1463)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1464]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₃(t)   (1464)

Precoding method determiner 316 performs the calculations described in“(precoding method (42A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1465} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (1465)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1466} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1466\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1466\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (42A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1467} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1467)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (42A)” is not satisfied.

(Precoding Method (42B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1468} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1468)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1469} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1469)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1470} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; {({\mu + \lambda})}} \times \cos \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; {({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; \mu} \times \sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; {({\mu + \lambda})}} \times \sin \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1470)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1471]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×sin θ=0  (1471-1)

h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×cosθ=0   (1471-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1472} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1472\text{-}1} \right) \\{\theta = {{- \delta} + \; \frac{\pi}{2}\mspace{11mu} + {n\; \pi \mspace{20mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1472\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1473} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1473\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1473\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1474]

|a| ² +|b| ² =|u| ²   (1474)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (42B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1475} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1475)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1476]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1062)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1477]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1477)

Precoding method determiner 316 performs the calculations described in“(precoding method (42B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1478} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1478)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1479} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1479\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1479\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (42B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1480} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1480)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1481]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1481)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1482]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1482)

Precoding method determiner 316 performs the calculations described in“(precoding method (42B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1483} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (1483)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1484} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1484\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1484\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (42B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{11mu} 1485} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1485)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (42B)” is not satisfied.

(Precoding Method (43A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1486} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1486)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1487} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1487)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1488} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1488)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1489]

−h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×sin θ−h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×cos θ=0  (1489-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×cos θ+h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0   (1489-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1490} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1490\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1490\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1491} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1491\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1491\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1492]

|a| ² +|b| ² =|u| ²   (1078)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (43A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1493} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1493)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1494]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1062)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1495]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1495)

Precoding method determiner 316 performs the calculations described in“(precoding method (43A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1496} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1496)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1497} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1497\text{-}1} \right) \\{and} & \; \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1497\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (43A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1498} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1498)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1499]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1499)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1500]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1500)

Precoding method determiner 316 performs the calculations described in“(precoding method (43A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1501} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j\; {({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (1501)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1502} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1502\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1502\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (43A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1503} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1503)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (43A)” is not satisfied.

(Precoding Method (43B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1504} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\; \sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1504)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1505} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j\; {({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1505)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1506} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{12}(t)}} \times \sin \; \delta} \\{{h_{21}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{12}(t)}} \times \sin \; \delta} \\{{h_{21}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j\; {({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j\; {({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; {({\omega + \lambda})}} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j\; {({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; {({\omega + \lambda})}} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; ɛ\; {(t)}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1506)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1507]

h ₁₁(t)×a×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×e ^(jω)×sin δ×sin θ=0   (1507-1)

−h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×sin θ+h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×cos θ=0  (1507-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1508} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1508\text{-}1} \right) \\{\theta = {{- \delta} + \; \frac{\pi}{2}\; + {n\; \pi \mspace{20mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1508\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1509} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1509\text{-}1} \right) \\{\theta = {{- \delta} + \; \frac{\pi}{2}\; + {n\; \pi \mspace{20mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1509\text{-}1} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1510]

|a| ² +|b| ² =|u| ²   (1510)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (43B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1511} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1511)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1512]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1512)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1513]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1513)

Precoding method determiner 316 performs the calculations described in“(precoding method (43B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1514} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j\; {({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times e^{j\; {({\mu + \lambda})}} \times \sin \; \theta} \\{b \times e^{j\; \omega} \times \sin \; \theta} & {b \times e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1514)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1515} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1515\text{-}1} \right) \\{\theta = {{- \delta} + \; \frac{\pi}{2}\; + {n\; \pi \mspace{20mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1515\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (43B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1516} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1516)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1517]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1517)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1518]

y ₂(t)=q ₂₁ ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1518)

Precoding method determiner 316 performs the calculations described in“(precoding method (43B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1519} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \cos \; \theta} & {{- e^{j\; {({\mu + \lambda})}}} \times \sin \; \theta} \\{e^{j\; \omega} \times \sin \; \theta} & {e^{j\; {({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (1519)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1520} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1520\text{-}1} \right) \\{\theta = {{- \delta} + \; \frac{\pi}{2}\; + {n\; \pi \mspace{20mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1520\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (43B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1521} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1521)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (43B)” is not satisfied.

(Precoding Method (44A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1522} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1522)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1523} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1523)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1524} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \; \cos \; \theta} -} & {{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta} & {{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta} \\{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \; \cos \; \theta} +} & {{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta} & {{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1524)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1525]

−h ₁₁(t)×a×β×e ^(jμ+λ))×cos δ×sin θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×cosθ=0   (1525-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×cos θ−h ₂₂(t)×b×β×e ^(jω)×cos δ×sin θ=0  (1525-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1526} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1526\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1526\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1527} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1527\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1527\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1528]

|a| ² +|b| ² =|u| ²   (1528)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (44A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1529} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1529)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1530]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1530)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1531]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1531)

Precoding method determiner 316 performs the calculations described in“(precoding method (44A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1532} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1532)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1533} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1533\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1533\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (44A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1534} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1534)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1535]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1535)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1536]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1536)

Precoding method determiner 316 performs the calculations described in“(precoding method (44A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1537} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (1537)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1538} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1538\text{-}1} \right) \\{\theta = {{- \delta} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1538\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (44A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1539} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1539)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (44A)” is not satisfied.

(Precoding Method (44B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1540} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1540)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1541} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1541)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1542} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \; \cos \; \theta} -} & {{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \sin \; \theta} & {{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \cos \; \theta} \\{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \; \cos \; \theta} +} & {{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \sin \; \theta} & {{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \cos \; \theta}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1542)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1543]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×cos θ−h ₂₂(t)×b×β∴e ^(jω)×sin δ×sin θ=0  (1543-1)

−h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×sin θ−h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×cos θ=0  (1543-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1544} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1544\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {1544\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1545} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1545\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1545\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1546]

|a| ² +|b| ² =|u| ²   (1546)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (44B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1547} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1547)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1548]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1548)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1549]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1549)

Precoding method determiner 316 performs the calculations described in“(precoding method (44B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1550} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \cos \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \sin \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}}\end{matrix} & (1550)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1551} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1551\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {1551\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (44B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1552} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1552)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1553]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1553)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1554]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1554)

Precoding method determiner 316 performs the calculations described in“(precoding method (44B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1555} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \cos \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \sin \; \theta} \\{\beta \times e^{j\; \omega} \times \sin \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \cos \; \theta}\end{pmatrix}} & (1555)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1556} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1556\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {1556\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (44B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1557} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \right.} \\{{\left. {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (1557)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (44B)” is not satisfied.

(Precoding Method (45A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1558} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1558)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1559} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{S_{1}(t)} \\{S_{2}(t)}\end{pmatrix}}} & (1559)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1560} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{= {{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{= {\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {\omega {(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu}\cos \; \delta \times} \\{{\sin \; \theta} - {{h_{22}(t)} \times}} \\{b \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} - {{h_{22}(t)} \times}} \\{b \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \omega}\sin \; \delta \times} \\{{\sin \; \theta} + {{h_{22}(t)} \times}}\end{matrix} \\{b \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} + {{h_{22}(t)} \times}} \\{b \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {\gamma {(t)}}}{s_{1}(t)}} \\{e^{{j\omega}{(t)}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1560)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1561]

−h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×sin θ=0  (1561-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×sin θ−h ₂₂(t)×b×e ^(jω)×cos δ×cos θ=0   (1561-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1562} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1562\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {1562\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1563} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}\mspace{14mu} {and}}} & \left( {1563\text{-}1} \right) \\{\theta = {{- \delta} + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}\mspace{14mu} \left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}} & \left( {1563\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1564]

|a| ² +|b| ² =|u| ²   (1564)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (45A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1565} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1565)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1566]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1566)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1567]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1567)

Precoding method determiner 316 performs the calculations described in“(precoding method (45A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1568} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1568)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1569} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1569\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1569\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (45A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1570} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1570)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1571]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1571)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1572]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1572)

Precoding method determiner 316 performs the calculations described in“(precoding method (45A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1573} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1573)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1574} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1574\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1574\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (45A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{85mu} {\left\lbrack {{MATH}.\mspace{14mu} 1575} \right\rbrack \mspace{695mu} (1575)}} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & \;\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andhx_(y, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (45A)” is not satisfied.

(Precoding Method (45B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1576} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1576)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1577} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1577)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}{\; \left\lbrack {{MATH}.\mspace{14mu} 1578} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu}} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu}} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{- {h_{11}(t)}} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1578)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1579]

h ₁₁(t)×a×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (1579-1)

−h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ+h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (1579-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1580} \right\rbrack & \; \\\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} \\{and}\end{matrix} & \left( {1580\text{-}1} \right) \\\begin{matrix}{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)\end{matrix} & \left( {1580\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

[MATH.  1581] $\begin{matrix}{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1581\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1581\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1582]

|a| ² +|b| ² =|u| ²   (1582)

(|u|² is a parameter based on average transmitted power)

Note that, regarding mapped baseband signal s₁(t) and mapped basebandsignal s₂(t), phase-change is implemented, but the configuration “mappedbaseband signal s₁(t) is not affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) is not affected(interference) by mapped baseband signal s₁(t)” is maintained.

(Precoding Method (45B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1583} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1583)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1584]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1584)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(0).

[MATH. 1585]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1585)

Precoding method determiner 316 performs the calculations described in“(precoding method (45B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1586} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {b \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1586)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1587} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1587\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1587\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (45B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1588} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1588)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1589]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1589)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1590]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1590)

Precoding method determiner 316 performs the calculations described in“(precoding method (45B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1591} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {{- e^{j{({\mu + \lambda})}}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1591)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1592} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1592\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1592\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (45B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{85mu} {\left\lbrack {{MATH}.\mspace{14mu} 1593} \right\rbrack \mspace{706mu} (1593)}} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & \;\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (45B)” is not satisfied.

(Precoding Method (46A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1594} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} +}} \\{\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1594)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1595} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1595)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\; \left\lbrack {{MATH}.\mspace{14mu} 1596} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \; \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}\begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu}\cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu}\sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{- {h_{11}(t)}} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1596)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1597]

−h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×sinθ=0   (1597-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×cos δ×cos θ=0  (1597-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1598} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1598\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{11mu} {integer}} \right)}}}} & \left( {1598\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1599} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1599\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1599\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1600]

|a| ² +|b| ² =|u| ²   (1600)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (46A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1601} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1601)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1602]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1602)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1603]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1603)

Precoding method determiner 316 performs the calculations described in“(precoding method (46A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1604} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {{{- a} \times \beta \times e^{j{({\mu + \lambda})}}} + {\cos \; \theta}} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1604)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1605} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1605\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1605\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (46A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1606} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1606)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1607]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1607)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1608]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1608)

Precoding method determiner 316 performs the calculations described in“(precoding method (46A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1609} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1609)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1610} \right\rbrack & \; \\{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}} & \left( {1610\text{-}1} \right) \\{and} & \; \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1610\text{-}2} \right) \\\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right) & \;\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (46A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγt))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

  [MATH.  1611] (1611) $\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (46A)” is not satisfied.

(Precoding Method (46B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1612} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1612)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1613} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1613)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1614} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; \mu} \times \cos \; \delta \times \; \sin \; \theta} -}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{h_{11}(t)} \times a \times \beta \times} \\{{e^{j\; \mu} \times \sin \; \delta \times \; \sin \; \theta} +}\end{matrix} & \begin{matrix}{{- {h_{11}(t)}} \times a \times \beta \times} \\{{e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{h_{22}(t)} \times b \times \beta \times} \\{e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1614)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1615]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×cos θ=0  (1615-1)

−h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×sinθ=0   (1615-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1616} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1616\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1616\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1617} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1617\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1617\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1618]

|a| ² +|b| ² =|u| ²   (1618)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (46B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is z₁(t).

Weighted signal 307B output by weighting synthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1619} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1619)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1620]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1620)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1621]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1621)

Precoding method determiner 316 performs the calculations described in“(precoding method (46B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1622} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \; \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {{- a} \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1622)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1623} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1623\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1623\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)).

Similarly, based on the values of q₂₁ and q₂₂, weighting synthesizer306B performs weighting synthesis calculations, and outputs weightedsignal 307B (z₂(t)).

(Precoding Method (46B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t).

Mapped signal 305B output by mapper 304B is s₂(t).

Weighted signal 307A output by weighting synthesizer 306A is y₁(t).

Weighted signal 307B output by weighting synthesizer 306B is y₂(t).

Coefficient multiplied signal 402A output by coefficient multiplier 401Ais z₁(t).

Coefficient multiplied signal 402B output by coefficient multiplier 401Bis z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1624} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1624)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1625]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1625)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1626]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1626)

Precoding method determiner 316 performs the calculations described in“(precoding method (46B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1627} \right\rbrack & \; \\{{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {{- \beta} \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {\beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\;} & (1627)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1628} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1628\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1628\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (46B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1629} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1629)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (46B)” is not satisfied.

(Precoding Method (47A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1630} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1630)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1631} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1631)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1632} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \; \sin \; \theta} -}\end{matrix} & \begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \; \sin \; \theta} +}\end{matrix} & \begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{e^{j\; {ɛ{(t)}}}{s_{1}(t)}} \\{e^{j\; {\gamma {(t)}}}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1632)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1633]

h ₁₁(t)×a×e ^(j(μ+λ))×cos δ×cos θ+h ₂₂(t)×b×e ^(j(ω+λ))×sin δ×sin θ=0  (1633-1)

h ₁₁(t)×a×e ^(jμ)×sin δ×sin θ−h ₂₂(t)×b×e ^(jω)×cos δ×sin θ=0   (1633-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1634} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1634\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1634\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1635} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1635\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1635\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1636]

|a| ² +|b| ² =|u| ²   (1636)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (47A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1637} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1637)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1638]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1638)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1639]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1639)

Precoding method determiner 316 performs the calculations described in“(precoding method (47A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1640} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1640)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1641} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1641\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1641\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (47A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1642} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1642)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1643]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1643)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1644]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1644)

Precoding method determiner 316 performs the calculations described in“(precoding method (47A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1645} \right) & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} & (1645)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1646} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1646\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1646\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (47A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1647} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}{{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}\end{pmatrix}} \\{{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1647)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (47A)” is not satisfied.

(Precoding Method (47B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1648} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1648)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1649} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1649)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1650} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} \\{{{\begin{pmatrix}{e^{j\; \delta}(t)} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times e^{j{({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times e^{j{({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{{e^{j\; \delta}(t)}{s_{1}(t)}} \\{{e^{j\; \gamma}(t)}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1650)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1651]

h ₁₁(t)×a×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×e ^(jω)×sin δ×cos θ=0   (1651-1)

h ₁₁(t)×a×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×e ^(j(ω+λ))×cos δ×sin θ=0  (1075-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1652} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1652\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1652\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1653} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1653\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1653\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1654]

|a| ² +|b| ² =|u| ²   (1654)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (47B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1655} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1655)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1656]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1656)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1657]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ +e ^(jγ(t)) ×s ₂(t)   (1657)

Precoding method determiner 316 performs the calculations described in“(precoding method (47B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1658} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times e^{j\; \mu} \times \sin \; \theta} & {a \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1658)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1659} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1659\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1659\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)).

Similarly, based on the values of q₂₁ and q₂₂, weighting synthesizer306B performs weighting synthesis calculations, and outputs weightedsignal 307B (z₂(t)).

(Precoding Method (47B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}{\; \left\lbrack {{MATH}.\mspace{14mu} 1660} \right\rbrack} & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1660)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1661]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1661)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1662]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1662)

Precoding method determiner 316 performs the calculations described in“(precoding method (47B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1663} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{e^{j\; \mu} \times \sin \; \theta} & {e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{e^{j\; \omega} \times \cos \; \theta} & {{- e^{j{({\omega + \lambda})}}} \times \sin \; \theta}\end{pmatrix}} & (1663)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1664} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1664\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1664\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (47B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1665} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}} = {{\left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} + {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}} & (1665)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andhx_(y, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (47B)” is not satisfied.

(Precoding Method (48A))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1666} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\; \sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1666)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1667} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1667)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following equation holds true.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1668} \right\rbrack} & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)}\; \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)}\; \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}}} \\{{\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}}} \\{{\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\cos \; \delta \times \sin \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\sin \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times} \\{{\cos \; \delta \times \cos \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times} \\{\sin \; \delta \times \sin \; \theta}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times} \\{{\sin \; \delta \times \sin \; \theta} +}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times} \\{\cos \; \delta \times \cos \; \theta}\end{matrix}\end{matrix} & \begin{matrix}\begin{matrix}{{h_{11}(t)} \times a \times \beta \times e^{j\; {({\mu + \lambda})}} \times} \\{{\sin \; \delta \times \cos \; \theta} -}\end{matrix} \\\begin{matrix}{{h_{22}(t)} \times b \times \beta \times e^{j\; {({\omega + \lambda})}} \times} \\{\cos \; \delta \times \sin \; \theta}\end{matrix}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}e^{j\; {ɛ{(t)}}} & {s_{1}(t)} \\e^{j\; {\gamma {(t)}}} & {s_{2}(t)}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1668)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1669]

h ₁₁(t)×a×β×e ^(j(μ+λ))×cos δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×sin δ×sinθ=0   (1669-1)

h ₁₁(t)×a×β×e ^(jμ)×sin δ×sin θ+h ₂₂(t)×b×β×e ^(jω)×cos δ×cos θ=0  (1669-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1670} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1670\text{-}1} \right) \\{\theta = {\delta + \; \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1670\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1671} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1671\text{-}1} \right) \\{\theta = {\delta + \; \frac{\pi}{2} + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1671\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1672]

|a| ² +|b| ² =|u| ²   (1672)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (48A-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1673} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1673)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1674]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1062)

Weighting synthesizer synthesizer 306B calculates the following andoutputs weighted signal 307B (z₂(t)).

[MATH. 1675]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1675)

Precoding method determiner 316 performs the calculations described in“(precoding method (48A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1676} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1676)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated.

Here, based on feedback information from a terminal, precoding methoddeterminer 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1677} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1677\text{-}1} \right) \\{\theta = {\delta + \; \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1677\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (48A-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1678} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1678)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1679]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1679)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1680]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1680)

Precoding method determiner 316 performs the calculations described in“(precoding method (48A)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1681} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1681)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1682} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1682\text{-}1} \right) \\{\theta = {\delta + \frac{\pi}{2} + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1682\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (48A))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1683} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \right.} \\{{\left. {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (1683)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andh_(xy, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (48A)” is not satisfied.

(Precoding Method (48B))

In a state such as in FIG. 2, signals r₁(t), r₂(t) that are received bya reception device can be applied as follows (note that δ is greaterthan or equal to 0 radians and less than 2π radians).

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1684} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)}\cos \; \delta} & {{- {h_{22}(t)}}\sin \; \delta} \\{{h_{11}(t)}\sin \; \delta} & {{h_{22}(t)}\cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1684)\end{matrix}$

Here, when z₁(t)=s₁(t) and z₂(t)=s₂(t) (s₁(t) and s₂(t) are mappedbaseband signals), excluding when δ=0, π/2, π, or 3π/2 radians, sincemapped baseband signal s₁(t) is affected (interference) by mappedbaseband signal s₂(t) and mapped baseband signal s₂(t) is affected(interference) by mapped baseband signal s₁(t), there is a possibilitythat data reception quality may decrease.

In light of this, presented is a method of performing precoding based onfeedback information obtained from a terminal by the communicationsstation. Consider a case in which precoding that uses a unitary matrixis performed, such as the following.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{MATH}.\mspace{14mu} 1685} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}\begin{pmatrix}e^{j\; {ɛ{(t)}}} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1685)\end{matrix}$

However, a and b are complex numbers (may be actual numbers). j is animaginary unit, and γ(t) is an argument and a time function.

In this case, the following relation equation holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1686} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{\cos \; \delta} & {{- \sin}\; \delta} \\{\sin \; \delta} & {\cos \; \delta}\end{pmatrix}\begin{pmatrix}{h_{11}(t)} & 0 \\0 & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= {\begin{pmatrix}{{h_{11}(t)} \times \cos \; \delta} & {{- {h_{22}(t)}} \times \sin \; \delta} \\{{h_{11}(t)} \times \sin \; \delta} & {{h_{22}(t)} \times \cos \; \delta}\end{pmatrix}\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{{{\begin{pmatrix}{e^{j\; \delta}(t)} & 0 \\0 & e^{j\; {\gamma {(t)}}}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \begin{pmatrix}\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \cos \; \delta \times \sin \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \sin \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \delta \times \cos \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \delta \times \sin \; \theta}\end{matrix} \\\begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j\; \mu} \times \sin \; \delta \times \sin \; \theta} +} \\{{h_{22}(t)} \times b \times \beta \times e^{j\; \omega} \times \cos \; \delta \times \cos \; \theta}\end{matrix} & \begin{matrix}{{{h_{11}(t)} \times a \times \beta \times e^{j{({\mu + \lambda})}} \times \sin \; \delta \times \cos \; \theta} -} \\{{h_{22}(t)} \times b \times \beta \times e^{j{({\omega + \lambda})}} \times \cos \; \delta \times \sin \; \theta}\end{matrix}\end{pmatrix}} \\{{\begin{pmatrix}{{e^{j\; \delta}(t)}{s_{1}(t)}} \\{{e^{j\; \gamma}(t)}{s_{2}(t)}}\end{pmatrix} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}}\end{matrix} & (1686)\end{matrix}$

In the above equation, as one method for preventing mapped basebandsignal s₁(t) from being affected (interference) by mapped basebandsignal s₂(t) and mapped baseband signal s₂(t) from being affected(interference) by mapped baseband signal s₁(t), there are the followingconditional equations.

[MATH. 1687]

h ₁₁(t)×a×β×e ^(jμ)×cos δ×sin θ−h ₂₂(t)×b×β×e ^(jω)×sin δ×cos θ=0  (1687-1)

h ₁₁(t)×a×β×e ^(j(μ+λ))×sin δ×cos θ−h ₂₂(t)×b×β×e ^(j(ω+λ))×cos δ×sinθ=0   (1687-2)

Accordingly, it is sufficient if the following holds true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1688} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1688\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1688\text{-}2} \right)\end{matrix}$

Accordingly, the communications station calculates θ, a, and b from thefeedback information from the terminal so that the following is true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1689} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1689\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {radians}}}} & \left( {1689\text{-}2} \right)\end{matrix}$

The communications station performs the precoding using these values.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Note that because of the average transmitted power, the followingrelation equation holds true.

[MATH. 1690]

|a| ² +|b| ² =|u| ²   (1690)

(|u|² is a parameter based on average transmitted power)

Note that phase-change is applied to both mapped baseband signal s₁(t)and mapped baseband signal s₂(t), but the configuration “mapped basebandsignal s₁(t) is not affected (interference) by mapped baseband signals₂(t) and mapped baseband signal s₂(t) is not affected (interference) bymapped baseband signal s₁(t)” is maintained.

(Precoding Method (48B-1))

FIG. 12 illustrates a configuration of a communications station. Oneexample of processes performed by weighting synthesizers 306A, 306B, andprecoding method determiner 316 illustrated in FIG. 12 will bedescribed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is z₁(t). Weighted signal 307B output by weightingsynthesizer 306B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1691} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1691)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (z₁(t)).

[MATH. 1692]

z ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1062)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (z₂(t)).

[MATH. 1693]

z ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1693)

Precoding method determiner 316 performs the calculations described in“(precoding method (48B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1694} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}} \\{= \begin{pmatrix}{a \times \beta \times e^{j\; \mu} \times \sin \; \theta} & {a \times \beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{b \times \beta \times e^{j\; \omega} \times \cos \; \theta} & {{- b} \times \beta \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}}\end{matrix} & (1694)\end{matrix}$

In other words, the precoding matrix of the above equation iscalculated. Here, based on feedback information from a terminal,precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1695} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1695\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1695\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(z₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (z₂(t)).

(Precoding Method (48B-2))

FIG. 13 illustrates a configuration of a communications stationdifferent from FIG. 12. One example of processes performed by weightingsynthesizers 306A, 306B, coefficient multipliers 401A, 401B, andprecoding method determiner 316 illustrated in FIG. 13 will bediscussed.

Mapped signal 305A output by mapper 304A is s₁(t). Mapped signal 305Boutput by mapper 304B is s₂(t). Weighted signal 307A output by weightingsynthesizer 306A is y₁(t). Weighted signal 307B output by weightingsynthesizer 306B is y₂(t). Coefficient multiplied signal 402A output bycoefficient multiplier 401A is z₁(t). Coefficient multiplied signal 402Boutput by coefficient multiplier 401B is z₂(t).

The precoding matrix is expressed as follows.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1696} \right\rbrack & \; \\\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} & (1696)\end{matrix}$

Accordingly, weighting synthesizer 306A calculates the following andoutputs weighted signal 307A (y₁(t)).

[MATH. 1697]

y ₁(t)=q ₁₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₁₂ ×e ^(jγ(t)) ×s ₂(t)   (1697)

Weighting synthesizer 306B calculates the following and outputs weightedsignal 307B (y₂(t)).

[MATH. 1698]

y ₂(t)=q ₂₁ ×e ^(jϵ(t)) ×s ₁(t)+q ₂₂ ×e ^(jγ(t)) ×s ₂(t)   (1698)

Precoding method determiner 316 performs the calculations described in“(precoding method (48B)” based on feedback information from a terminal,and determines the precoding matrix.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1699} \right\rbrack & \; \\{\begin{pmatrix}q_{11} & q_{12} \\q_{21} & q_{22}\end{pmatrix} = \begin{pmatrix}{\beta \times e^{j\; \mu} \times \sin \; \theta} & {\beta \times e^{j{({\mu + \lambda})}} \times \cos \; \theta} \\{\beta \times e^{j\; \omega} \times \cos \; \theta} & {{- \beta} \times e^{j{({\omega + \lambda})}} \times \sin \; \theta}\end{pmatrix}} & (1699)\end{matrix}$

In other words, the precoding matrix of the above equation and valuesfor a and b are calculated. Here, based on feedback information from aterminal, precoding method determiner 316 uses

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1700} \right\rbrack & \; \\{{b = {\frac{h_{11}(t)}{h_{22}(t)} \times a \times e^{j{({\mu - \omega})}}}}{and}} & \left( {1700\text{-}1} \right) \\{\theta = {\delta + {n\; \pi \mspace{20mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}}}} & \left( {1700\text{-}2} \right)\end{matrix}$

to determine a, b, and θ, to determine the precoding matrix.

For example, the communications station transmits a training symbol, andthe terminal performs channel estimation from the training symbol andprovides the channel estimation value to the communications station asfeedback. The communications station then calculates the values for θ,a, and b by using the information provided as feedback.

Based on the values of q₁₁ and q₁₂, weighting synthesizer 306A performsweighting synthesis calculations, and outputs weighted signal 307A(y₁(t)). Similarly, based on the values of q₂₁ and q₂₂, weightingsynthesizer 306B performs weighting synthesis calculations, and outputsweighted signal 307B (y₂(t)).

Then, coefficient multiplier 401A illustrated in FIG. 13 receives aninput of weighted signal 307A (y₁(t)), calculates z₁(t)=a×y₁(t), andoutputs coefficient multiplied signal 402A (z₁(t)). Similarly,coefficient multiplier 401B illustrated in FIG. 13 receives an input ofweighting synthesized signal 307B (y₂(t)), calculates z₂(t)=b×y₂(t), andoutputs coefficient multiplied signal 402B (z₂(t)).

(Phase Changing in Precoding Method (48B))

Phase changer 1001A illustrated in FIG. 12 and FIG. 13 receives an inputof mapped signal s₁(t) output from mapper 304A, applies a phase-change,and outputs phase-changed signal 1002A (e^(jϵ(t))×s₁(t)). Phase changer1001B illustrated in FIG. 12 and FIG. 13 receives an input of mappedsignal s₂(t) output from mapper 304B, applies a phase-change, andoutputs phase-changed signal 1002B (e^(jγ(t))×s₂(t)).

In FIG. 2, when fluctuation in an antenna state is rapid, for example,when the antenna is vibrating due to, for example, wind or the terminalbeing used on the move, there is no guarantee that the value of δ inFIG. 2 can be kept substantially constant in the frame. Accordingly, itis likely that the following relation equation will hold true.

$\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1701} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{r_{1}(t)} \\{r_{2}(t)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}} \\{= \left( {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}{h_{11,d}(t)} & {h_{12,d}(t)} \\{h_{21,d}(t)} & {h_{22,d}(t)}\end{pmatrix}} +} \right.} \\{{\left. {\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(t)} & {h_{12,s}(t)} \\{h_{21,s}(t)} & {h_{22,s}(t)}\end{pmatrix}} \right)\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix}} + \begin{pmatrix}{n_{1}(t)} \\{n_{2}(t)}\end{pmatrix}}\end{matrix} & (1701)\end{matrix}$

Here, h_(xy, d)(t) is a direct wave component of h_(xy)(t), andhx_(y, s)(t) is a scattered wave component of h_(xy)(t). (x=1, 2; y=1,2) K is a Rice factor.

A case in which Rice factor K is large will be discussed. Here, channelfluctuation tends to be small due to influence from direct waves.Accordingly, when phase-change is not implemented—that is to say, whenphase changer 1001A and phase changer 1001B are not provided in FIG. 12and FIG. 13—in the reception device, it is likely that r₁(t) and r₂(t)are in a continuous (small amount of fluctuation) reception state.Accordingly, regardless of the reception field intensity being high,there is a possibility of being continuously in a state in which signaldemultiplexing is difficult.

On the other hand, in FIG. 12 and FIG. 13, when phase changer 1001A andphase changer 1001B are present, in the reception device, since r₁(t)and r₂(t) are implemented with a time (or frequency) phase-change by thetransmission device, they can be kept from being in continuous receptionstate. Accordingly, it is likely that continuously being in a state inwhich signal demultiplexing is difficult can be avoided.

As described above, in either of the two different channel states, it ispossible to achieve a superior advantageous effect, namely that afavorable state reception quality can be achieved. Note that in FIG. 12and FIG. 13, when the phase changer is arranged after the weightingsynthesizer, “precoding method (48B)” is not satisfied.

(Phase Change Method)

In the description hereinbefore, the value γ(t), ϵ(t) relating to phasechange is, but not limited to, being applied as a function of t (t:time). For example, when the communications station illustrated in FIG.10 and FIG. 11 transmits a multi-carrier, such as orthogonal frequencydivision multiplexing

(OFDM), modulated signal, the value y(t), c(t) relating to phase changemay be applied as a function of “frequency” or as a function of “timeand frequency”. Accordingly, when frequency is express as f, when thevalue relating to phase change is a function of “frequency”, it isexpressed as γ(f), ϵ(f), and when the value relating to phase change isa function of “time and frequency”, it is expressed as γ(f, t), ϵ(f, t).

Hereinafter, examples of applications of phase change γ(t), ϵ(t); γ(f),ϵ(f); and γ(f, t), ϵ(f, t) will be given.

(Phase Change Method (1))

FIG. 14 illustrates one example of a phase change method, extractingrelevant portions from phase changer 1001B and weighting synthesizers306A, 306B illustrated in FIG. 10.

Phase change is performed in phase changer 1001B; a change example isillustrated in FIG. 14.

For example, with symbol number #u (since phase change value γ istreated as a function of a symbol number, it is written as γ(u)), phasechange value γ(u)=e^(j0) is applied. Accordingly, weighting synthesizers306A and 306B receive inputs of s₁(u) and γ(u)×s₂(u).

With symbol number #(u+1), phase change value γ(u+1)=e^((j×1×π)/2) isapplied. Accordingly, weighting synthesizers 306A and 306B receiveinputs of s₁(u+1) and γ(u+1)×s₂(u+1).

With symbol number #(u+2), phase change value γ(u+2)=e^((j×2×π)/2) isapplied. Accordingly, weighting synthesizers 306A and 306B receiveinputs of s₁(u+2) and γ(u+2)×s₂(u+2).

With symbol number #(u+3), phase change value γ(u+3)=e^((j×3×π)/2) isapplied. Accordingly, weighting synthesizers 306A and 306B receiveinputs of s₁(u+3) and γ(u+3)×s₂(u+3).

With symbol number #(u+k), phase change value γ(u+k)=e^((j×k×π)/2) isapplied. (For example, k is an integer.) Accordingly, weightingsynthesizers 306A and 306B receive inputs of s₁(u+k) and γ(u 30k)×s₂(u+k).

(Note that the above description is applicable to any of: when thesymbols are arranged in the time axis direction, when the symbols arearranged in the frequency axis direction, and when the symbols arearranged in the time/frequency axis direction.)

Then, at time $1 of modulated signal z₁(t), z₁(t) of symbol number #u istransmitted, and at time $1 of modulated signal z₂(t), z₂(t) of symbolnumber #u is transmitted.

At time $2 of modulated signal z₁(t), z₁(t) of symbol number #(u+1) istransmitted, and at time $2 of modulated signal z₂(t), z₂(t) of symbolnumber #(u+1) is transmitted.

Note that z₁(t) and z₂(t) are transmitted from different antennas usingthe same frequency.

(Phase Change Method (2))

FIG. 15 illustrates one example of a phase change method, extractingrelevant portions from phase changer 1001B, weighting synthesizers 306A,306B, and coefficient multipliers 401A, 401B illustrated in FIG. 11.

Phase change is performed in phase changer 1001B; a change example isillustrated in FIG. 15.

For example, with symbol number #u (since phase change value γ istreated as a function of a symbol number, it is written as γ(u)), phasechange value γ(u)=e^(j0) is applied. Accordingly, weighting synthesizers306A and 306B receive inputs of s₁(u) and γ(u)×s₂(u).

With symbol number #(u+1), phase change value γ(u+1)=e^((j×1×π)/2) isapplied. Accordingly, weighting synthesizers 306A and 306B receiveinputs of s₁(u+1) and γ(u+1)×s₂(u+1).

With symbol number #(u+2), phase change value γ(u+2)=e^((j×2×π)/2) isapplied. Accordingly, weighting synthesizers 306A and 306B receiveinputs of s₁(u+2) and γ(u+2)×s₂(u+2).

With symbol number #(u+3), phase change value γ(u+3)=e^((j×3×π)/2) isapplied. Accordingly, weighting synthesizers 306A and 306B receiveinputs of s₁(u+3) and γ(u+3)×s₂(u+3).

With symbol number #(u+k), phase change value γ(u+k)=e^((j×k×π)/2) isapplied. (For example, k is an integer.) Accordingly, weightingsynthesizers 306A and 306B receive inputs of s₁(u+k) and γ(u+k)×s₂(u+k).

Note that the above description is applicable to any of: when thesymbols are arranged in the time axis direction, when the symbols arearranged in the frequency axis direction, and when the symbols arearranged in the time/frequency axis direction.

Then, at time $1 of modulated signal z₁(t), z₁(t) of symbol number #u istransmitted, and at time $1 of modulated signal z₂(t), z₂(t) of symbolnumber #u is transmitted.

At time $2 of modulated signal z₁(t), z₁(t) of symbol number #(u+1) istransmitted, and at time $2 of modulated signal z₂(t), z₂(t) of symbolnumber #(u+1) is transmitted.

Note that z₁(t) and z₂(t) are transmitted from different antennas usingthe same frequency.

(Frame Configuration (1))

Next, an example of a frame configuration when the phase change value isa function of frequency fthat is to say, when the phase change value isexpressed as γ(f)—will be described.

Here, the phase change value of symbol number #0 is expressed as y(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on.(In other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs₁(k) and γ(k)×s₂(k)).

FIG. 16 is one example of a frame configuration when the symbols arearranged in the frequency direction.

In FIG. 16, (A) illustrates one example of a frame configuration ofmodulated signal z₁, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 16, carriers 0 through 9 and symbols fortime $1 and time $2 are shown. Note that the symbols for z₁ and z₂ inthe same carrier number at the same time are transmitted from differentantennas at the same time and at the same frequency.

In FIG. 16, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 16, the symbol for symbol number #0 of z₁ isarranged at time $1, carrier 0; the symbol for symbol number #5 of z₁ isarranged at time $1, carrier 1; and the symbol for symbol number #1 ofz₁ is arranged at time $1, carrier 2. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #17 of z₁ is arranged at time $2, carrier 5).

Moreover, in (B) in FIG. 16, the symbol for symbol number #0 of z₂ isarranged at time $1, carrier 0; the symbol for symbol number #5 of z₂ isarranged at time $1, carrier 1; and the symbol for symbol number #1 ofz₂ is arranged at time $1, carrier 2. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #17 of z₂ is arranged at time $2, carrier 5).

(Frame Configuration (2))

Next, an example of a frame configuration when the phase change value isa function of time t, frequency f—that is to say, when the phase changevalue is expressed as γ(t, f)—will be described.

Here, the phase change value of symbol number #0 is expressed as γ(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on(in other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs₁(k) and γ(k)×s₂(k)).

FIG. 17 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 17, (A) illustrates one example of a frame configuration ofmodulated signal z₁, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z₂, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 17, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor zi and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 17, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words,“-Ap” means it is a symbol for symbol number #p (for example, p is aninteger greater than or equal to 0)).

Accordingly, in (A) in FIG. 17, the symbol for symbol number #0 of z₁ isarranged at time $1, carrier 0; the symbol for symbol number #1 of z₁ isarranged at time $1, carrier 1; and the symbol for symbol number #2 ofz₁ is arranged at time $2, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #19 of z1 is arranged at time $2, carrier 5).

Moreover, in (B) in FIG. 17, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $1, carrier 1; and the symbol for symbol number #2 ofz2 is arranged at time $2, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #19 of z2 is arranged at time $2, carrier 5).

(Frame Configuration (3))

Next, a different example of a frame configuration when the phase changevalue is a function of time t, frequency f—that is to say, when thephase change value is expressed as y(t, f)—will be described.

Here, the phase change value of symbol number #0 is expressed as γ(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on.(In other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs₁(k) and γ(k)×s₂(k)).

FIG. 18 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 18, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z₂, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 18, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 18, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 18, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $2, carrier 0; and the symbol for symbol number #2 ofz1 is arranged at time $3, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #21 of z1 is arranged at time $2, carrier 5).

Moreover, in (B) in FIG. 18, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $2, carrier 0; and the symbol for symbol number #2 ofz2 is arranged at time $3, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #21 of z2 is arranged at time $2, carrier 5).

(Frame Configuration (4))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of time t—that is to say,as γ(t)—and a symbol other than a data symbol, such as a controlinformation symbol for transmitting control information or a pilotsymbol for channel estimation, frequency synchronization, timesynchronization, or signal detection (reference symbol, preamble) ispresent midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on.(In other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs1(k) and γ(k)×s2(k)).

FIG. 19 is one example of a frame configuration when the symbols arearranged in the time direction.

In FIG. 19, (A) illustrates one example of a frame configuration ofmodulated signal z1, where time is represented on the horizontal axis,and (B) illustrates one example of a frame configuration of modulatedsignal z2, where time is represented on the horizontal axis (note thatthe symbols for z1 and z2 at the same time are transmitted fromdifferent antennas at the same frequency).

In FIG. 19, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1. (In other words,“-Ap” means it is a symbol for symbol number #p (for example, p is aninteger greater than or equal to 0)). Moreover, “P” indicates a pilotsymbol (note that, here, “P” indicates a pilot symbol, but it mayindicate a symbol other than a pilot symbol (excluding a data symbol)).

Accordingly, in (A) in FIG. 19, the symbol for symbol number #0 of z1 isarranged at time $1; the symbol for symbol number #1 of z1 is arrangedat time $2; the symbol for symbol number #2 of z1 is arranged at time$3; and a pilot symbol is arranged at time $4. Note that the othersymbols are also arranged according to the same rules.

Moreover, in (B) in FIG. 19, the symbol for symbol number #0 of z1 isarranged at time $1; the symbol for symbol number #1 of z1 is arrangedat time $2; and the symbol for symbol number #2 of z1 is arranged attime $3. Note that the other symbols are also arranged according to thesame rules.

Note that in the example illustrated in FIG. 19, with symbols other thandata symbols, a phase-change is not applied.

(Frame Configuration (5))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of frequency fthat is tosay, as γ(f)—and a symbol other than a data symbol, such as a controlinformation symbol for transmitting control information or a pilotsymbol for channel estimation, frequency synchronization, timesynchronization, or signal detection (reference symbol, preamble) ispresent midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on(in other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs₁(k) and γ(k)×s₂(k)).

FIG. 20 is one example of a frame configuration when the symbols arearranged in the frequency direction.

In FIG. 20, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 20, carriers 0 through 9 and symbols fortime $1 and time $2 are shown (note that the symbols for z1 and z2 inthe same carrier number at the same time are transmitted from differentantennas at the same time and at the same frequency).

In FIG. 20, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 20, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; a pilot symbol is arranged at time $1,carrier 1; a pilot symbol is arranged at time $1, carrier 2; and thesymbol for symbol number #1 of z1 is arranged at time $1, carrier 3.Note that the other symbols are also arranged according to the samerules.

Moreover, in (B) in FIG. 20, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; a pilot symbol is arranged at time $1,carrier 1; a pilot symbol is arranged at time $1, carrier 2; and thesymbol for symbol number #1 of z2 is arranged at time $1, carrier 3.Note that the other symbols are also arranged according to the samerules.

Note that in the example illustrated in FIG. 20, with symbols other thandata symbols, a phase-change is not applied.

(Frame Configuration (6))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of time t, frequencyf—that is to say, as γ(t, f)—and a symbol other than a data symbol, suchas a control information symbol for transmitting control information ora pilot symbol for channel estimation, frequency synchronization, timesynchronization, or signal detection (reference symbol, preamble) ispresent midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on(in other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs₁(k) and γ(k)×s₂(k)).

FIG. 21 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 21, (A) illustrates one example of a frame configuration ofmodulated signal z₁, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 21, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 21, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 21, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $1, carrier 1; the symbol for symbol number #2 of z1 isarranged at time $2, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Moreover, in (B) in FIG. 21, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $1, carrier 1; the symbol for symbol number #2 of z2 isarranged at time $2, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Note that in the example illustrated in FIG. 21, with symbols other thandata symbols, a phase-change is not applied.

(Frame Configuration (7))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of time t, frequencyf—that is to say, as γ(t, f)—and a symbol other than a data symbol, suchas a control information symbol for transmitting control information ora pilot symbol for channel estimation, frequency synchronization, timesynchronization, or signal detection (reference symbol, preamble) ispresent midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),the phase change value of symbol number #1 is expressed as γ(1), thephase change value of symbol number #2 is expressed as γ(2), and so on(in other words, the phase change value of symbol number #k is expressedas γ(k) (k is an integer greater than or equal to 0). Accordingly, insymbol number #k, weighting synthesizers 306A and 306B receive inputs ofs₁(k) and γ(k)×s₂(k)).

FIG. 22 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 22, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 22, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 22, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 22, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $2, carrier 0; the symbol for symbol number #2 of z1 isarranged at time $3, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Moreover, in (B) in FIG. 22, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $2, carrier 0; the symbol for symbol number #2 of z2 isarranged at time $3, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Note that in the example illustrated in FIG. 22, with symbols other thandata symbols, a phase-change is not applied.

(Phase Change Method (3))

FIG. 23 illustrates one example of a phase change method, extractingrelevant portions from phase changers 1001A, 1001B and weightingsynthesizers 306A, 306B illustrated in FIG. 12.

Phase change is performed in phase changers 1001A, 1001B; a changeexample is illustrated in FIG. 23.

For example, with symbol number #u (since phase change value γ istreated as a function of a symbol number, it is written as γ(u); sincephase change value ϵ is treated as a function of a symbol number, it iswritten as E(u)), phase change value γ(u)=e^(j0) is applied, and phasechange value ϵ(u)=e^(j((−0×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u)×s₁(u) andγ(u)×s₂(u).

With symbol number #(u+1), phase change value γ(u+1)=e^((j×1×π)/4) isapplied, and ϵ(u+1)=e^(j((−1×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u+1)×s₁(u+1)and γ(u+1)×s₂(u+1).

With symbol number #(u+2), phase change value γ(u+2)=e^((j×2×π)/4) isapplied, and ϵ(u+2)=e^(j((−2×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u+2)×s₁(u+2)and γ(u+2)×s₂(u+2).

With symbol number #(u+3), phase change value γ(u+3)=e^((j×3×π)/4) isapplied, and ϵ(u+3)=e^(j((−3×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u+3)×s₁(u+3)and γ(u+3)×s₂(u+3).

With symbol number #(u+k), phase change value γ(u+k)=e^((j×k×π)/4) isapplied, and ϵ(u+k)=e^(j(−k×π/4)−(π/2))) is applied. (For example, k isan integer.) Accordingly, weighting synthesizers 306A and 306B receiveinputs of ϵ(u+k)×s₁(u+k) and γ(u+k)×s₂(u+k).

Note that the above description is applicable to any of: when thesymbols are arranged in the time axis direction, when the symbols arearranged in the frequency axis direction, and when the symbols arearranged in the time/frequency axis direction.

Then, at time $1 of modulated signal z₁(t), z₁(t) of symbol number #u istransmitted, and at time $1 of modulated signal z₂(t), z₂(t) of symbolnumber #u is transmitted.

At time $2 of modulated signal z₁(t), z₁(t) of symbol number #(u+1) istransmitted, and at time $2 of modulated signal z₂(t), z₂(t) of symbolnumber #(u+1) is transmitted.

Note that z₁(t) and z₂(t) are transmitted from different antennas usingthe same frequency.

(Phase Change Method (4))

FIG. 24 illustrates one example of a phase change method, extractingrelevant portions from 1001A, 1001B, weighting synthesizers 306A, 306B,and coefficient multipliers 401A, 401B illustrated in FIG. 13.

Phase change is performed in phase changers 1001A, 1001B; a changeexample is illustrated in FIG. 24.

For example, with symbol number #u (since phase change value γ istreated as a function of a symbol number, it is written as γ(u); sincephase change value ϵ is treated as a function of a symbol number, it iswritten as ϵ(u)), phase change value γ(u)=e^(j0) is applied, and phasechange value ϵ(u)=e^(j((−0×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u)×s₁(u) andγ(u)×s₂(u).

With symbol number #(u+1), phase change value γ(u+1)=e^((j×1×π)/4) isapplied, and ϵ(u+1)=e^(j((−1×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of c(u+1)×s₁(u+1)and γ(u+1)×s₂(u+1).

With symbol number #(u+2), phase change value γ(u+2)=e^((j×2×π)/4) isapplied, and ϵ(u+2)=e^(j((−2×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u+2)×s₁(u+2)and γ(u+2)×s₂(u+2).

With symbol number #(u+3), phase change value γ(u+3)=e^((j×3×π)/4) isapplied, and ϵ(u+3)=e^(j((−3×π/4)−(π/2))) is applied. Accordingly,weighting synthesizers 306A and 306B receive inputs of ϵ(u+3)×s₁(u+3)and γ(u+3)×s₂(u+3).

With symbol number #(u+k), phase change value γ(u+k)=e^((j×k×π)/4) isapplied, and ϵ(u+k)=e^(j((−k×π/4)−(π/2))) is applied. (For example, k isan integer.) Accordingly, weighting synthesizers 306A and 306B receiveinputs of c(u+k)×s₁(u+k) and γ(u+k)×s₂(u+k).

Note that the above description is applicable to any of: when thesymbols are arranged in the time axis direction, when the symbols arearranged in the frequency axis direction, and when the symbols arearranged in the time/frequency axis direction.

Then, at time $1 of modulated signal z z₁(t) of symbol number #u istransmitted, and at time $1 of modulated signal z₂(t), z₂(t) of symbolnumber #u is transmitted.

At time $2 of modulated signal z₁(t), z₁(t) of symbol number #(u +1) istransmitted, and at time $2 of modulated signal z₂(t), z₂(t) of symbolnumber #(u+1) is transmitted.

Note that z₁(t) and z₂(t) are transmitted from different antennas usingthe same frequency.

(Frame Configuration (8))

Next, an example of a frame configuration when the phase change value isa function of frequency f—that is to say, when the phase change value isexpressed as γ(f), ϵ(f)—will be described.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k), ϵ(k) (k is an integer greater than or equal to0). Accordingly, in symbol number #k, weighting synthesizers 306A and306B receive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(k)).

FIG. 16 is one example of a frame configuration when the symbols arearranged in the frequency direction.

In FIG. 16, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 16, carriers 0 through 9 and symbols fortime $1 and time $2 are shown. Note that the symbols for z₁ and z₂ inthe same carrier number at the same time are transmitted from differentantennas at the same time and at the same frequency.

In FIG. 16, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 16, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #5 of z1 isarranged at time $1, carrier 1; and the symbol for symbol number #1 ofz1 is arranged at time $1, carrier 2. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #17 of z1 is arranged at time $2, carrier 5).

Moreover, in (B) in FIG. 16, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #5 of z2 isarranged at time $1, carrier 1; and the symbol for symbol number #1 ofz2 is arranged at time $1, carrier 2. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #17 of z2 is arranged at time $2, carrier 5).

(Frame Configuration (9))

Next, an example of a frame configuration when the phase change value isa function of time t, frequency f—that is to say, when the phase changevalue is expressed as γ(t, f), ϵ(t, f)—will be described.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k), ϵ(k) (k is an integer greater than or equal to0). Accordingly, in symbol number #k, weighting synthesizers 306A and306B receive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(k)).

FIG. 17 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 17, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z₂, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 17, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 17, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 17, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $1, carrier 1; and the symbol for symbol number #2 ofz1 is arranged at time $2, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #19 of z1 is arranged at time $2, carrier 5).

Moreover, in (B) in FIG. 17, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $1, carrier 1; and the symbol for symbol number #2 ofz2 is arranged at time $2, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #19 of z2 is arranged at time $2, carrier 5).

(Frame Configuration (10))

Next, a different example of a frame configuration when the phase changevalue is a function of time t, frequency f—that is to say, when thephase change value is expressed as γ(t, f), ϵ(t, f)—will be described.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k) (k is an integer greater than or equal to 0).Accordingly, in symbol number #k, weighting synthesizers 306A and 306Breceive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(10).

FIG. 18 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 18, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z₂, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 18, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 18, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 18, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $2, carrier 0; and the symbol for symbol number #2 ofz1 is arranged at time $3, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #21 of z1 is arranged at time $2, carrier 5).

Moreover, in (B) in FIG. 18, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $2, carrier 0; and the symbol for symbol number #2 ofz2 is arranged at time $3, carrier 0. Note that the other symbols arealso arranged according to the same rules (for example, the symbol forsymbol number #21 of z2 is arranged at time $2, carrier 5).

(Frame Configuration (11))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of time t—that is to say,as γ(t), ϵ(t)—and a symbol other than a data symbol, such as a controlinformation symbol for transmitting control information or a pilotsymbol for channel estimation, frequency synchronization, timesynchronization, or signal detection (reference symbol, preamble) ispresent midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k), ϵ(k) (k is an integer greater than or equal to0). Accordingly, in symbol number #k, weighting synthesizers 306A and306B receive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(k)).

FIG. 19 is one example of a frame configuration when the symbols arearranged in the time direction.

In FIG. 19, (A) illustrates one example of a frame configuration ofmodulated signal z1, where time is represented on the horizontal axis,and (B) illustrates one example of a frame configuration of modulatedsignal z2, where time is represented on the horizontal axis (note thatthe symbols for z1 and z2 at the same time are transmitted fromdifferent antennas at the same frequency).

In FIG. 19, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1. (In other words,“#p” means it is a symbol for symbol number p (for example, p is aninteger greater than or equal to 0)). Moreover, “P” indicates a pilotsymbol (note that, here, “P” indicates a pilot symbol, but it mayindicate a symbol other than a pilot symbol (excluding a data symbol)).

Accordingly, in (A) in FIG. 19, the symbol for symbol number #0 of z1 isarranged at time $1; the symbol for symbol number #1 of z1 is arrangedat time $2; the symbol for symbol number #2 of z1 is arranged at time$3; and a pilot symbol is arranged at time $4. Note that the othersymbols are also arranged according to the same rules.

Moreover, in (B) in FIG. 19, the symbol for symbol number #0 of z1 isarranged at time $1; the symbol for symbol number #1 of z1 is arrangedat time $2; and the symbol for symbol number #2 of z1 is arranged attime $3. Note that the other symbols are also arranged according to thesame rules.

Note that in the example illustrated in FIG. 19, with symbols other thandata symbols, a phase-change is not applied.

(Frame Configuration (12))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of frequency f—that is tosay, as γ(f), ϵ(f)—and a symbol other than a data symbol, such as acontrol information symbol for transmitting control information or apilot symbol for channel estimation, frequency synchronization, timesynchronization, or signal detection (reference symbol, preamble) ispresent midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k), ϵ(k) (k is an integer greater than or equal to0). Accordingly, in symbol number #k, weighting synthesizers 306A and306B receive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(k)).

FIG. 20 is one example of a frame configuration when the symbols arearranged in the frequency direction.

In FIG. 20, (A) illustrates one example of a frame configuration ofmodulated signal z₁, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 20, carriers 0 through 9 and symbols fortime $1 and time $2 are shown (note that the symbols for z1 and z2 inthe same carrier number at the same time are transmitted from differentantennas at the same time and at the same frequency).

In FIG. 20, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number -4p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 20, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; a pilot symbol is arranged at time $1,carrier 1; a pilot symbol is arranged at time $1, carrier 2; and thesymbol for symbol number #1 of z1 is arranged at time $1, carrier 3.Note that the other symbols are also arranged according to the samerules.

Moreover, in (B) in FIG. 20, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; a pilot symbol is arranged at time $1,carrier 1; a pilot symbol is arranged at time $1, carrier 2; and thesymbol for symbol number #1 of z2 is arranged at time $1, carrier 3.Note that the other symbols are also arranged according to the samerules.

Note that in the example illustrated in FIG. 20, with symbols other thandata symbols, a phase-change is not applied.

(Frame Configuration (13))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of time t, frequencyf—that is to say, as γ(t, f), ϵ(t, f)—and a symbol other than a datasymbol, such as a control information symbol for transmitting controlinformation or a pilot symbol for channel estimation, frequencysynchronization, time synchronization, or signal detection (referencesymbol, preamble) is present midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k), ϵ(k) (k is an integer greater than or equal to0). Accordingly, in symbol number #k, weighting synthesizers 306A and306B receive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(k)).

FIG. 21 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 21, (A) illustrates one example of a frame configuration ofmodulated signal z1, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 21, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 21, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 21, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $1, carrier 1; the symbol for symbol number #2 of z1 isarranged at time $2, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Moreover, in (B) in FIG. 21, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $1, carrier 1; the symbol for symbol number #2 of z2 isarranged at time $2, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Note that in the example illustrated in FIG. 21, with symbols other thandata symbols, a phase-change is not applied.

(Frame Configuration (14))

Next, an example of a frame configuration will be given in which thephase change value is expressed as a function of time t, frequencyf—that is to say, as γ(t, f), ϵ(t, f)—and a symbol other than a datasymbol, such as a control information symbol for transmitting controlinformation or a pilot symbol for channel estimation, frequencysynchronization, time synchronization, or signal detection (referencesymbol, preamble) is present midway through.

Here, the phase change value of symbol number #0 is expressed as γ(0),ϵ(0), the phase change value of symbol number #1 is expressed as γ(1),ϵ(1), the phase change value of symbol number #2 is expressed as γ(2),ϵ(2), and so on (in other words, the phase change value of symbol number#k is expressed as γ(k), ϵ(k) (k is an integer greater than or equal to0). Accordingly, in symbol number #k, weighting synthesizers 306A and306B receive inputs of ϵ(k)×s₁(k) and γ(k)×s₂(k)).

FIG. 22 is one example of a frame configuration when the symbols arearranged in the time/frequency direction.

In FIG. 22, (A) illustrates one example of a frame configuration ofmodulated signal z₁, where frequency is represented on the horizontalaxis and time is represented on the vertical axis, and (B) illustratesone example of a frame configuration of modulated signal z2, wherefrequency is represented on the horizontal axis and time is representedon the vertical axis. In FIG. 22, carriers 0 through 9 and symbols fortime $1, time $2, time $3, and time $4 are shown (note that the symbolsfor z1 and z2 in the same carrier number at the same time aretransmitted from different antennas at the same time and at the samefrequency).

In FIG. 22, for example, “#0” means it is a symbol for symbol number #0,and “#1” means it is a symbol for symbol number #1 (in other words, “#p”means it is a symbol for symbol number #p (for example, p is an integergreater than or equal to 0)).

Accordingly, in (A) in FIG. 22, the symbol for symbol number #0 of z1 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z1 isarranged at time $2, carrier 0; the symbol for symbol number #2 of z1 isarranged at time $3, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Moreover, in (B) in FIG. 22, the symbol for symbol number #0 of z2 isarranged at time $1, carrier 0; the symbol for symbol number #1 of z2 isarranged at time $2, carrier 0; the symbol for symbol number #2 of z2 isarranged at time $3, carrier 0; and a pilot symbol is arranged at time$2, carrier 2. Note that the other symbols are also arranged accordingto the same rules.

Note that in the example illustrated in FIG. 22, with symbols other thandata symbols, a phase-change is not applied.

(Phase Change Description)

Hereinbefore, the performing of phase-change has been described, buthere, how the phase-change is applied will be described by way ofexamples.

Here, when phase change value γ is a function of symbol number i, thisis expressed as γ(i), and when phase change value ϵ is a function ofsymbol number i, this is expressed as ϵ(i). Here, γ(i) and ϵ(i) are notconstant values (the y fluctuate according to symbol number).

Accordingly, the following relation equations are satisfied.

-   γ(i) ≠ g (g is a constant complex number (may be an actual number)).-   ϵ(i) ≠ h (h is a constant complex number (may be an actual number)).

Phase change value γ(i) and phase change value ϵ(i) are preferably setso as to be periodic relative to be a symbol number.

For example, five types of phases are prepared as phase change values.

The five types of phase change values are Phase [0], Phase [1], Phase[2], Phase [3], and Phase [4].

Then,

-   when i mod 5=0: γ(i)=Phase [0];-   when i mod 5=1: γ(i)=Phase [1]:-   when i mod 5=2: γ(i)=Phase [2];-   when i mod 5=3: γ(i)=Phase [3]; and-   when i mod 5=4: γ(i)=Phase [4].-   “mod” is an abbreviation for “modulo” and “i mod 5” means “remainder    when i is divided by 5”.

With this, phase change value γ(i) is periodic relative to a symbolnumber (here, the number of periods is five, but the value for thenumber of periods may be another value (the number of periods is aninteger greater than or equal to 2)).

Similarly, for example, three types of phases are prepared as phasechange values. The three types of phase change values are Phase_x [0],Phase_x [1], and Phase_x [2].

Then,

-   when i mod 3=0: ϵ(i)=Phase_x [0];-   when i mod 3=1: ϵ(i)=Phase_x [1]; and-   when i mod 3=2: ϵ(i)=Phase_x [2].-   “mod” is an abbreviation for “modulo” and “i mod 5” means “remainder    when i is divided by 5”.

With this, phase change value ϵ(i) is periodic relative to a symbolnumber (here, the number of periods is three, but the value for thenumber of periods may be another value (the number of periods is aninteger greater than or equal to 2)).

Moreover, for example, when the number of periods of the phase changevalue is N, N types of phases are prepared. Then, that value is Phase[k] (k is an integer that is greater than or equal to 0 and less than orequal to N−1 (N is an integer that is greater than or equal to 2)).

Here, in order to satisfy u ≠ v, the following may hold true for each uand each v.

-   Phase [u] ≠ Phase [v]

Moreover, a different method is conceivable in which u ≠ v; u and vwhich satisfy Phase [u] =Phase [v] are present, but N periods areformed.

As a different method, phase-change may be performed without usingperiods under a condition that “γ(i) and ϵ(i) are not constant values”is satisfied.

(Mapper Description)

In FIG. 3, FIG. 4, FIG. 10, FIG. 11, FIG. 12, and FIG. 13, mappers 304Aand 304B are illustrated as being separate from one another, but amapper may be arranged as illustrated in FIG. 25.

In FIG. 25, mapper 2502 receives an input of bit sequence 2501, andoutputs mapped signals 305A and 305B.

The advantages of this configuration will be described next. Forexample, the modulation method of modulated signal s₁(i) is QPSK, andthe modulation method of modulated signal s₂(i) is QPSK. 4 bits arerequired for one-symbol generation of modulated signal s₁(t) andone-symbol generation of modulated signal s₂(t). Here, the 4 bits areb_(1, 0), b_(1, 1), b_(1, 2), and b_(1, 3).

The first QPSK symbol generates, using bit sequences b_(1, 0) andb_(1, 1), an in-phase component I[1, 1] of an orthogonal baseband signaland an orthogonal component Q[1, 1] of an orthogonal baseband signal.The second QPSK symbol generates, using bit sequences b_(1, 2) andb_(1, 3), an in-phase component I[1, 2] of an orthogonal baseband signaland an orthogonal component Q[1, 2] of an orthogonal baseband signal.

The in-phase component of modulated signal s₁(i=1) is I[1, 1], and theorthogonal component of modulated signal s₁(i=1) is Q[1, 2]. Moreover,the in-phase component of modulated signal s₂(i=1) is I[1, 2], and theorthogonal component of modulated signal s₂(i=1) is Q[1, 2].

In other words, the first QPSK symbol generates, using bit sequencesb_(k, 0) and b_(k, 1), an in-phase component I[k, 1] of an orthogonalbaseband signal and an orthogonal component Q[k, 1] of an orthogonalbaseband signal. The second QPSK symbol generates, using bit sequencesb_(k, 2) and b_(k, 3), an in-phase component I[k, 2] of an orthogonalbaseband signal and an orthogonal component Q[k, 2] of an orthogonalbaseband signal.

The in-phase component of modulated signal s1(i=1) is I[k, 1], and theorthogonal component of modulated signal s1(i=1) is Q[k, 2]. Moreover,the in-phase component of modulated signal s₂(i=1) is I[k, 2], and theorthogonal component of modulated signal s₂(i=1) is Q[k, 1].

With this, the bit sequences b_(k, 0), b_(k, 1), b_(k, 2), and b_(k, 3)are advantageous in that they can achieve a high diversity effect sincethey are transmitted from a plurality of antennas.

Note that in the above examples, the modulation method is exemplified asQPSK, but the modulation method may be Quadrature Amplitude Modulation(16 QAM), 64 QAM, 256 QAM, Amplitude Phase Shift Keying (16 APSK), 64APSK, 256 APSK, Non-uniform QAM (NU-QAM), or NU mapping. The sameprocesses are applied when any of these methods are used. Moreover, thesame processes are performed regardless of whether the modulation methodof modulated signal s1(i) and the modulation method of modulated signals2(i) are the same or different.

In other words, “an in-phase component I[k, 1] of a first mappedorthogonal baseband signal and an orthogonal component Q[k, 1] of theorthogonal baseband signal are generated from a first bit sequence. Anin-phase component I[k, 2] of a second mapped orthogonal baseband signaland an orthogonal component Q[k, 2] of the orthogonal baseband signalare generated from a second bit sequence. An in-phase component ofmodulated signal s₁(i=1) is I[k, 1], and an orthogonal component is Q[k,2]. Moreover, an in-phase component of modulated signal s₂(i=1) is I[k,2], and an orthogonal component is Q[k, 1].”

(Communications Station Configuration (5))

In FIG. 3, FIG. 10, and FIG. 12, a rearranger may be inserted betweenthe weighting synthesizer and the radio unit.

FIG. 26 illustrates an example of such a configuration. Rearranger 2602Areceives inputs of weighted signal 307A and transmission method/frameconfiguration signal 319, and rearranges weighted signal 307A based ontransmission method/frame configuration signal 319 to output rearrangedsignal 2603A. For example, it is possible to realize a possiblerearrangement of the symbols in FIG. 16 and FIG. 22.

Rearranger 2602B receives inputs of weighted signal 307B andtransmission method/frame configuration signal 319, and rearrangesweighted signal 307B based on transmission method/frame configurationsignal 319 to output rearranged signal 2603B. For example, it ispossible to realize a possible rearrangement of the symbols in FIG. 16and FIG. 22.

In FIG. 4, FIG. 11, and FIG. 13, a rearranger may be inserted betweenthe coefficient multiplier and the radio unit.

FIG. 27 illustrates an example of such a configuration. Rearranger 2602Areceives inputs of coefficient multiplied signal 402A and transmissionmethod/frame configuration signal 319, and rearranges coefficientmultiplied signal 402A based on transmission method/frame configurationsignal 319 to output rearranged signal 2603A. For example, it ispossible to realize a possible rearrangement of the symbols in FIG. 16and FIG. 22. Note that it is possible to switch the order of rearranger2602A and coefficient multiplier 401A.

Rearranger 2602B receives inputs of coefficient multiplied signal 402Band transmission method/frame configuration signal 319, and rearrangescoefficient multiplied signal 402B based on transmission method/frameconfiguration signal 319 to output rearranged signal 2603B. For example,it is possible to realize a possible rearrangement of the symbols inFIG. 16 and FIG. 22. Note that it is possible to switch the order ofrearranger 2602B and coefficient multiplier 401B.

(Supplemental Information)

In FIG. 1 and FIG. 2, a configuration in which communication isperformed using horizontal polarizing antennas and vertical polarizingantennas on the transmitting side and receiving side is illustrated, butthe transmission method according to this disclosure is not limitedthereto. For example, the transmission method can be applied to whencommunication is performed using two different types of polarizingantennas with respect to the transmitting side and receiving side.

Moreover, taking into consideration the polarization states of thetransmitting side and the receiving side, in order to satisfy conditionsfor preventing mapped baseband signal s₁(t) from being affected(interference) by mapped baseband signal s₂(t) and mapped basebandsignal s₂(t) from being affected (interference) by mapped basebandsignal s₁(t), the value of θ in the precoding is determined, but factorsother than polarization may also be considered when determining thevalue of θ.

As a matter of course, the present disclosure may be carried out bycombining two or more of the embodiments and other subject matterdescribed herein.

Moreover, the embodiments are merely examples. For example, while a“modulation method, an error correction coding method (error correctioncode, code length, encode rate, etc., to be used), control information,etc.” are exemplified, it is possible to carry out the presentdisclosure with the same configuration even when other types of a“modulation method, an error correction coding method (error correctioncode, code length, encode rate, etc., to be used), control information,etc.” are applied.

Regarding the modulation method, even when a modulation method otherthan the modulation methods described herein is used, it is possible tocarry out the embodiments and the other subject matter described herein.For example, Amplitude Phase Shift Keying (APSK) (such as 16 APSK, 64APSK, 128 APSK, 256 APSK, 1024 APSK and 4096 APSK), Pulse AmplitudeModulation (PAM) (such as 4 PAM, 8 PAM, 16 PAM, 64 PAM, 128 PAM, 256PAM, 1024 PAM and 4096 PAM), Phase Shift Keying (PSK) (such as BPSK,QPSK, 8 PSK, 16 PSK, 64 PSK, 128 PSK, 256 PSK, 1024 PSK and 4096 PSK),and Quadrature Amplitude Modulation (QAM) (such as 4 QAM, 8 QAM, 16 QAM,64 QAM, 128 QAM, 256 QAM, 1024 QAM and 4096 QAM) may be applied, or ineach modulation method, uniform mapping or non-uniform mapping may beperformed. Moreover, a method for arranging 2, 4, 8, 16, 64, 128, 256,1024, etc., signal points on an I-Q plane (a modulation method having 2,4, 8, 16, 64, 128, 256, 1024, etc., signal points) is not limited to asignal point arrangement method of the modulation methods describedherein.

Herein, it can be considered that communications and broadcastapparatuses such as a broadcast station, a base station, an accesspoint, a terminal and a mobile phone includes the transmission device.In these cases, it can be considered that a communication apparatus suchas a television, a radio, a terminal, a personal computer, a mobilephone, an access point and a base station includes the reception device.Moreover, it can also be considered that the transmission device andreception device according to the present disclosure are each a devicehaving communication functions and is formed so as to be connectable viasome interface to an apparatus for executing an application in, forexample, a television, a radio, a personal computer or a mobile phone.Moreover, in this embodiment, symbols other than data symbols, such aspilot symbols (preamble, unique word, post-amble, reference symbol,etc.) or symbols for control information, may be arranged in any way ina frame. Here, the terms “pilot symbol” and “control information” areused, but the naming of such symbols is not important; the functionsthat they perform are.

A pilot symbol may be a known symbol that is modulated using PSKmodulation in a transceiver (alternatively, a symbol transmitted by atransmitter can be known by a receiver by the receiver being periodic),and the receiver detects, for example, frequency synchronization, timesynchronization, and a channel estimation (Channel State Information(CSI)) symbol (of each modulated signal) by using the symbol.

Moreover, the symbol for control information is a symbol fortransmitting information required to be transmitted to a communicationpartner in order to establish communication pertaining to anything otherthan data (such as application data) (this information is, for example,the modulation method, error correction coding method, or encode rate ofthe error correction coding method used in the communication, orsettings information in an upper layer).

Note that the present disclosure is not limited to each exemplaryembodiment, and can be carried out with various modifications. Forexample, in each embodiment, the present disclosure is described asbeing performed as a communications device. However, the presentdisclosure is not limited to this case, and this communications methodcan also be used as software.

Note that a program for executing the above-described communicationsmethod may be stored in Read Only Memory (ROM) in advance to cause aCentral Processing Unit (CPU) to operate this program.

Moreover, the program for executing the communications method may bestored in a computer-readable storage medium, the program stored in therecording medium may be recorded in Random Access Memory (RAM) in acomputer, and the computer may be caused to operate according to thisprogram.

Each configuration of each of the above-described embodiments, etc., maybe realized as a Large Scale Integration (LSI) circuit, which istypically an integrated circuit. These integrated circuits may be formedas separate chips, or may be formed as one chip so as to include theentire configuration or part of the configuration of each embodiment.

LSI is described here, but the integrated circuit may also be referredto as an IC (Integrated Circuit), a system LSI circuit, a super LSIcircuit or an ultra LSI circuit depending on the degree of integration.Moreover, the circuit integration technique is not limited to LSI, andmay be realized by a dedicated circuit or a general purpose processor.After manufacturing of the LSI circuit, a programmable FieldProgrammable Gate Array (FPGA) or a reconfigurable processor which isreconfigurable in connection or settings of circuit cells inside the LSIcircuit may be used. Further, when development of a semiconductortechnology or another derived technology provides a circuit integrationtechnology which replaces LSI, as a matter of course, functional blocksmay be integrated by using this technology. Adaption of biotechnology,for example, is a possibility.

In the present specification, examples in which horizontal polarizingantennas and vertical polarizing antennas are used are given, but theseexamples are not limiting. For example, even if clockwise rotationcircular polarizing antennas and counterclockwise rotation circularpolarizing antennas are used, “changing the weighting synthesizingmethod and/or coefficient multiplication method based on feedbackinformation from a communication partner (for example, weightingsynthesizers 306A, 306B) in, for example, FIG. 3, and coefficientmultipliers 401A, 401B in, for example, FIG. 4)” described in thepresent specification can be implemented (in other words, theconfiguration method of the antennas is not limited).

Moreover, in the present specification, specific methods forcalculating, based on feedback information from a communication partner,the parameter θ in a precoding matrix in a weighted synthesizing methodthe parameters a and b in the precoding matrix, and the parameters a andb in a coefficient multiplier were described, but the calculation methodis not limited to the above described methods. Accordingly, so long as aconfiguration in which a communications station sets, based on feedbackinformation from a communication partner, the parameter θ in a precodingmatrix in a weighted synthesizing method and/or parameters a and b inthe precoding matrix, and/or parameters a and b in a coefficientmultiplier (at least one of the parameter θ in a precoding matrix in aweight synthesizing method, parameters a and b in the precoding matrix,and parameters a and b in a coefficient multiplier), generates amodulated signal based on the settings, and transmits the modulatedsignal to the communication partner, the advantageous effects describedin the present specification are obtainable. Note that the timing of theswitching between the above-described parameters may be arbitrarily set,such as set to be performed on a per frame basis or per unit time basis.The setting of the above-described parameters may be performed by thecommunications station and may be instructed by the communicationpartner. Then, the values for θ, a, and b used by the communicationsstation are notified to the communication partner by using, for example,control information symbols. With this, the communication partnerdemodulates the control information symbols to know the values for θ, a,and b used by the communications station, and with this, thedemodulation/decoding of the data symbols is possible.

In the present specification, parameters a and b were described, butwhen there is a great difference in the absolute values of parameters aand b a device that displays a warning screen or an audio generator forgenerating a warning sound for notifying of “there is a great differencein the absolute values of parameters a and b” may be included incommunications station. This is because when “there is a greatdifference in the absolute values of parameters a and b”, resetting theantennas is likely to increase communication quality.

In the present specification, upon setting the values for parameters θ,a, and b, the communications station may perform a method that selectsfrom a table stored in the communications station sets values forparameters θ, a, and b. Hereinafter an example will be given.

For example, a table is prepared including θ0, θ1, θ2, and θ3 as valuesfor selectable parameter θ. Then the communications station selects anappropriate value from among θ0, θ1, θ2, and θ3, and sets the value forparameter θ.

Similarly, a table is prepared including a0, a1, a2, and a3 as valuesfor selectable parameter a. Then the communications station selects anappropriate value from among a0, a1, a2, and a3, and sets the value forparameter a.

A table is prepared including b0, b1, b2, and b3 as values forselectable parameter b. Then the communications station selects anappropriate value from among b0, b1, b2, and b3, and sets the value forparameter b.

Here, four types of values are presented as selectable values, but thisexample is not limiting.

Moreover, when control information x=x0, this is associated with “set θ0as value for θ”; when control information x=x1, this is associated with“set θ1 as value for θ”; when control information x=x2, this isassociated with “set θ2 as value for θ”; and when control informationx=x3, this is associated with “set θ3 as value for θ”. Accordingly, bythe communications station transmitting control information x as controlinformation to a communication partner, the communication partner canknow the value of θ used by the communications station.

Similarly, when control information y=y0, this is associated with “seta0 as value for a”; when control information y=y1, this is associatedwith “set a1 as value for a”; when control information y=y2, this isassociated with “set a2 as value for a”; and when control informationy=y3, this is associated with “set a3 as value for a”. Accordingly, bythe communications station transmitting control information y as controlinformation to a communication partner, the communication partner canknow the value of a used by the communications station.

When control information z=z0, this is associated with “set b0 as valuefor b”; when control information z=z1, this is associated with “set b1as value for b”; when control information z=z2, this is associated with“set b2 as value for b”; and when control information z=z3, this isassociated with “set b3 as value for b”. Accordingly, by thecommunications station transmitting control information z as controlinformation to a communication partner, the communication partner canknow the value of b used by the communications station.

INDUSTRIAL APPLICABILITY

The present disclosure can be used in polarized MIMO systems.

REFERENCE MARKS IN THE DRAWINGS

300, 400 communications station

306A, 306B weighting synthesizer

401A, 402B coefficient multiplier

1. A transmission method, comprising: generating and transmitting afirst transmission signal z₁(t) and a second transmission signal z₂(t)by calculating Equation (1): $\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 1} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1)\end{matrix}$ from a first modulated signal s₁(t) and a second modulatedsignal s₂(t); and calculating θ, a, and b based on feedback informationso as to satisfy: $\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 2} \right\rbrack & \; \\{b = {{\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}\mspace{14mu} \theta} = {{- \delta} + {n\; {\pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}.}}}}} & \;\end{matrix}$
 2. A transmission device that: generates and transmits afirst transmission signal z₁(t) and a second transmission signal z₂(t)by calculating Equation (1): $\begin{matrix}\left\lbrack {{MATH}.\mspace{14mu} 3} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(t)} \\{z_{2}(t)}\end{pmatrix} = {\begin{pmatrix}a & 0 \\0 & b\end{pmatrix}\begin{pmatrix}{\cos \; \theta} & {\sin \; \theta} \\{\sin \; \theta} & {{- \cos}\; \theta}\end{pmatrix}\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix}}} & (1)\end{matrix}$ from a first modulated signal s₁(t) and a second modulatedsignal s₂(t); and calculates θ, a, and b based on feedback informationso as to satisfy: $\begin{matrix}{b = {{\frac{h_{11}(t)}{h_{22}(t)} \times a\mspace{14mu} {and}\mspace{14mu} \theta} = {{- \delta} + {n\; {\pi \mspace{14mu} {{radians}\left( {n\mspace{14mu} {is}\mspace{14mu} {an}\mspace{14mu} {integer}} \right)}.}}}}} & \left\lbrack {{MATH}.\mspace{14mu} 4} \right\rbrack\end{matrix}$